Finite Group Databasebeta

← Group #10729201

Character table — Group #10729201

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11111111111111112222222222222222444444444444666666668888888888888888888888888888888888881212121212121212121212122424242424242424
order1222222222222222366666666666666644444444444422222222444444441212121212121212121212121212121212121212121212121212121244444444444422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222220000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111-1-1-1-1111100000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2000000002222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111111100000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-200000000-2-2-2-22222-1-1-1-1111111111111-1-1-1-11111-1-1-1-100000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-20000000022-2-2-2-2221111-1-1-1-1-1-1-1-1111111111111-1-1-1-100000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-200000000-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222220000000022-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222200000000-2-222-2-222111111111111-1-1-1-11111-1-1-1-1-1-1-1-100000000000000000000
χ25222222-2-2-2-2-22-2-2-22222222-2-2-2-22-2-2-2-220000000000002222-2-2-2-22i−2i000000000000002i2i−2i−2i0000000000000000000000000000002i−2i0000
χ26222222-2-2-2-2-22-2-2-22222222-2-2-2-22-2-2-2-220000000000002222-2-2-2-2−2i2i00000000000000−2i−2i2i2i000000000000000000000000000000−2i2i0000
χ27222222-2-2-2-2-22-2-2-22222222-2-2-2-22-2-2-2-22000000000000-2-2-2-222222i−2i000000000000002i2i−2i−2i000000000000000000000000000000−2i2i0000
χ28222222-2-2-2-2-22-2-2-22222222-2-2-2-22-2-2-2-22000000000000-2-2-2-22222−2i2i00000000000000−2i−2i2i2i0000000000000000000000000000002i−2i0000
χ292222-2-22-2-22-2-222-2-22222-2-22-2-2-2-2222-2-2000000002i2i−2i−2i0000000000000000000000000000000000002i2i−2i−2i00002i2i−2i−2i22-2-2000000000000
χ302222-2-22-2-22-2-222-2-22222-2-22-2-2-2-2222-2-2000000002i2i−2i−2i0000000000000000000000000000000000002i2i−2i−2i0000−2i−2i2i2i-2-222000000000000
χ312222-2-22-2-22-2-222-2-22222-2-22-2-2-2-2222-2-200000000−2i−2i2i2i000000000000000000000000000000000000−2i−2i2i2i00002i2i−2i−2i-2-222000000000000
χ322222-2-22-2-22-2-222-2-22222-2-22-2-2-2-2222-2-200000000−2i−2i2i2i000000000000000000000000000000000000−2i−2i2i2i0000−2i−2i2i2i22-2-2000000000000
χ3322-2-222-22-22-2-22-22-222-2-222-22-2-2-222-22-22i2i−2i−2i0000000000000000000000002i2i−2i−2i00000000000000000000000000002-22-22i2i−2i−2i00000000
χ3422-2-222-22-22-2-22-22-222-2-222-22-2-2-222-22-22i2i−2i−2i0000000000000000000000002i2i−2i−2i0000000000000000000000000000-22-22−2i−2i2i2i00000000
χ3522-2-222-22-22-2-22-22-222-2-222-22-2-2-222-22-2−2i−2i2i2i000000000000000000000000−2i−2i2i2i00000000000000000000000000002-22-2−2i−2i2i2i00000000
χ3622-2-222-22-22-2-22-22-222-2-222-22-2-2-222-22-2−2i−2i2i2i000000000000000000000000−2i−2i2i2i0000000000000000000000000000-22-222i2i−2i−2i00000000
χ3722-2-2-2-222-2-2-22-222222-2-2-2-222-2-22-2-222200000000000022-2-222-2-20000002-200000000000000000000000022-2-20000000000002-2000000
χ3822-2-2-2-222-2-2-22-222222-2-2-2-222-2-22-2-222200000000000022-2-222-2-2000000-22000000000000000000000000-2-222000000000000-22000000
χ3922-2-2-2-222-2-2-22-222222-2-2-2-222-2-22-2-2222000000000000-2-222-2-2220000002-200000000000000000000000022-2-2000000000000-22000000
χ4022-2-2-2-222-2-2-22-222222-2-2-2-222-2-22-2-2222000000000000-2-222-2-222000000-22000000000000000000000000-2-2220000000000002-2000000
χ4122-2-2-2-2-2-222222-2-2222-2-2-2-2-2-222222-2-22000022-2-2000022-2-2-2-22200000000000022-2-20000000000000000000000002-2-22000000000000
χ4222-2-2-2-2-2-222222-2-2222-2-2-2-2-2-222222-2-22000022-2-20000-2-22222-2-200000000000022-2-2000000000000000000000000-222-2000000000000
χ4322-2-2-2-2-2-222222-2-2222-2-2-2-2-2-222222-2-220000-2-222000022-2-2-2-222000000000000-2-222000000000000000000000000-222-2000000000000
χ4422-2-2-2-2-2-222222-2-2222-2-2-2-2-2-222222-2-220000-2-2220000-2-22222-2-2000000000000-2-2220000000000000000000000002-2-22000000000000
χ452-22-22-2222-2-2-22-2-222-22-22-2222-2-22-2-2-220000000000002-22-22-22-200002i−2i0000000000000000002i2i−2i−2i000000000000000000000000002i−2i
χ462-22-22-2222-2-2-22-2-222-22-22-2222-2-22-2-2-220000000000002-22-22-22-20000−2i2i000000000000000000−2i−2i2i2i00000000000000000000000000−2i2i
χ472-22-22-2222-2-2-22-2-222-22-22-2222-2-22-2-2-22000000000000-22-22-22-2200002i−2i0000000000000000002i2i−2i−2i00000000000000000000000000−2i2i
χ482-22-22-2222-2-2-22-2-222-22-22-2222-2-22-2-2-22000000000000-22-22-22-220000−2i2i000000000000000000−2i−2i2i2i000000000000000000000000002i−2i
χ492-22-22-2-2-2-222-2-22222-22-22-2-2-2-22-2-22222000000002-22-22-22-2-22-2200000000000000000000000000002-22-20000000000002-22-200000000
χ502-22-22-2-2-2-222-2-22222-22-22-2-2-2-22-2-22222000000002-22-2-22-222-22-200000000000000000000000000002-22-2000000000000-22-2200000000
χ512-22-22-2-2-2-222-2-22222-22-22-2-2-2-22-2-2222200000000-22-222-22-2-22-220000000000000000000000000000-22-22000000000000-22-2200000000
χ522-22-22-2-2-2-222-2-22222-22-22-2-2-2-22-2-2222200000000-22-22-22-222-22-20000000000000000000000000000-22-220000000000002-22-200000000
χ532-22-2-22-2222-22-22-2-22-22-2-22-222-22-222-2-22-22-22i−2i2i−2i2i−2i−2i2i00000000000000002-22-22i−2i2i−2i0000000000002i−2i−2i2i000000000000000000000000
χ542-22-2-22-2222-22-22-2-22-22-2-22-222-22-222-2-22-22-2−2i2i−2i2i−2i2i2i−2i00000000000000002-22-2−2i2i−2i2i000000000000−2i2i2i−2i000000000000000000000000
χ552-22-2-22-2222-22-22-2-22-22-2-22-222-22-222-2-2-22-222i−2i2i−2i−2i2i2i−2i0000000000000000-22-222i−2i2i−2i000000000000−2i2i2i−2i000000000000000000000000
χ562-22-2-22-2222-22-22-2-22-22-2-22-222-22-222-2-2-22-22−2i2i−2i2i2i−2i−2i2i0000000000000000-22-22−2i2i−2i2i0000000000002i−2i−2i2i000000000000000000000000
χ572-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-1112-22-22i−2i2i−2i2i−2i−2i2i0000000000000000-11-11−ii−ii−i3i3−i3i3−i3−i3i3i33−33−3−iii−i3−33−300000000000000000000
χ582-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-1112-22-22i−2i2i−2i2i−2i−2i2i0000000000000000-11-11−ii−iii3−i3i3−i3i3i3−i3−i3−33−33−iii−i−33−3300000000000000000000
χ592-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-1112-22-2−2i2i−2i2i−2i2i2i−2i0000000000000000-11-11i−ii−i−i3i3−i3i3−i3−i3i3i3−33−33i−i−ii−33−3300000000000000000000
χ602-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-1112-22-2−2i2i−2i2i−2i2i2i−2i0000000000000000-11-11i−ii−ii3−i3i3−i3i3i3−i3−i33−33−3i−i−ii3−33−300000000000000000000
χ612-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-111-22-222i−2i2i−2i−2i2i2i−2i00000000000000001-11-1−ii−ii−i3i3−i3i3i3i3−i3−i3−33−33i−i−ii3−33−300000000000000000000
χ622-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-111-22-222i−2i2i−2i−2i2i2i−2i00000000000000001-11-1−ii−iii3−i3i3−i3−i3−i3i3i33−33−3i−i−ii−33−3300000000000000000000
χ632-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-111-22-22−2i2i−2i2i2i−2i−2i2i00000000000000001-11-1i−ii−i−i3i3−i3i3i3i3−i3−i33−33−3−iii−i−33−3300000000000000000000
χ642-22-2-22-2222-22-22-2-2-11-111-11-1-11-11-1-111-22-22−2i2i−2i2i2i−2i−2i2i00000000000000001-11-1i−ii−ii3−i3i3−i3−i3−i3i3i3−33−33−iii−i3−33−300000000000000000000
χ652-2-222-22-222-22-2-22-22-2-222-22-22-22-22-22-200002i−2i−2i2i0000000000000000000000002i−2i−2i2i000000000000000000002-22-200002i−2i−2i2i00000000
χ662-2-222-22-222-22-2-22-22-2-222-22-22-22-22-22-200002i−2i−2i2i0000000000000000000000002i−2i−2i2i00000000000000000000-22-220000−2i2i2i−2i00000000
χ672-2-222-22-222-22-2-22-22-2-222-22-22-22-22-22-20000−2i2i2i−2i000000000000000000000000−2i2i2i−2i000000000000000000002-22-20000−2i2i2i−2i00000000
χ682-2-222-22-222-22-2-22-22-2-222-22-22-22-22-22-20000−2i2i2i−2i000000000000000000000000−2i2i2i−2i00000000000000000000-22-2200002i−2i−2i2i00000000
χ692-2-22-2222-222-2-2-2-222-2-22-2222-22-2-22-2-222i−2i−2i2i000000002-2-222-2-22000000002i−2i−2i2i0000000000000000000000002i−2i−2i2i0000000000000000
χ702-2-22-2222-222-2-2-2-222-2-22-2222-22-2-22-2-222i−2i−2i2i00000000-222-2-222-2000000002i−2i−2i2i000000000000000000000000−2i2i2i−2i0000000000000000
χ712-2-22-2222-222-2-2-2-222-2-22-2222-22-2-22-2-22−2i2i2i−2i000000002-2-222-2-2200000000−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000000000000000
χ722-2-22-2222-222-2-2-2-222-2-22-2222-22-2-22-2-22−2i2i2i−2i00000000-222-2-222-200000000−2i2i2i−2i0000000000000000000000002i−2i−2i2i0000000000000000
χ732-2-22-22-2-22-2-2-222222-2-22-22-2-22-2-22-22220000000000002-2-22-222-2002-200000000000000002-22-200000000000000000000000000002-200
χ742-2-22-22-2-22-2-2-222222-2-22-22-2-22-2-22-22220000000000002-2-22-222-200-220000000000000000-22-220000000000000000000000000000-2200
χ752-2-22-22-2-22-2-2-222222-2-22-22-2-22-2-22-2222000000000000-222-22-2-22002-200000000000000002-22-20000000000000000000000000000-2200
χ762-2-22-22-2-22-2-2-222222-2-22-22-2-22-2-22-2222000000000000-222-22-2-2200-220000000000000000-22-2200000000000000000000000000002-200
χ77444444-4-4-4-4-44-4-4-44-2-2-2-2-2-22222-22222-2000000000000000000004i−4i00000000000000−2i−2i2i2i000000000000000000000000000000000000
χ78444444-4-4-4-4-44-4-4-44-2-2-2-2-2-22222-22222-200000000000000000000−4i4i000000000000002i2i−2i−2i000000000000000000000000000000000000
χ794444-4-44-4-44-4-444-4-4-2-2-2-222-22222-2-2-222000000004i4i−4i−4i000000000000000000000000000000000000−2i−2i2i2i000000000000000000000000
χ804444-4-44-4-44-4-444-4-4-2-2-2-222-22222-2-2-22200000000−4i−4i4i4i0000000000000000000000000000000000002i2i−2i−2i000000000000000000000000
χ814444-4-4-444-44-4-4-44-44444-4-4-4444-4-4-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ824444-4-4-444-44-4-4-44-4-2-2-2-2222-2-2-22222-2200000000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ834444-4-4-444-44-4-4-44-4-2-2-2-2222-2-2-22222-22000000000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ8444-4-4444-44-44-4-44-4-444-4-4444-444-4-4-44-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ8544-4-4444-44-44-4-44-4-4-2-222-2-2-22-2-2222-2220000000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ8644-4-4444-44-44-4-44-4-4-2-222-2-2-22-2-2222-22200000000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ8744-4-444-44-44-4-44-44-4-2-222-2-22-2222-2-22-224i4i−4i−4i000000000000000000000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ8844-4-444-44-44-4-44-44-4-2-222-2-22-2222-2-22-22−4i−4i4i4i0000000000000000000000002i2i−2i−2i00000000000000000000000000000000000000000000
χ8944-4-4-4-444-4-4-44-4444-2-22222-2-222-222-2-2-2000000000000000000000000004-4000000000000000000000000-2-22200000000000000000000
χ9044-4-4-4-444-4-4-44-4444-2-22222-2-222-222-2-2-200000000000000000000000000-4400000000000000000000000022-2-200000000000000000000
χ9144-4-4-4-4-4-444444-4-44-2-2222222-2-2-2-2-222-2000044-4-4000000000000000000000000-2-2220000000000000000000000000000000000000000
χ9244-4-4-4-4-4-444444-4-44-2-2222222-2-2-2-2-222-20000-4-44400000000000000000000000022-2-20000000000000000000000000000000000000000
χ934-44-44-4444-4-4-44-4-44-22-22-22-2-2-222-2222-20000000000000000000000004i−4i000000000000000000−2i−2i2i2i0000000000000000000000000000
χ944-44-44-4444-4-4-44-4-44-22-22-22-2-2-222-2222-2000000000000000000000000−4i4i0000000000000000002i2i−2i−2i0000000000000000000000000000
χ954-44-44-4-4-4-444-4-4444-22-22-22222-222-2-2-2-2000000004-44-4000000000000000000000000000000000000-22-22000000000000000000000000
χ964-44-44-4-4-4-444-4-4444-22-22-22222-222-2-2-2-200000000-44-440000000000000000000000000000000000002-22-2000000000000000000000000
χ974-44-4-444-4-4-4444-44-44-44-4-444-4-4444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44-4-444-4-4-4444-44-4-22-222-2-222-2-2-222-2200000000000000000000000000000000000023−23−2323000000000000000000000000000000000000
χ994-44-4-444-4-4-4444-44-4-22-222-2-222-2-2-222-22000000000000000000000000000000000000−232323−23000000000000000000000000000000000000
χ1004-4-444-44-444-44-4-44-4-222-2-22-22-22-22-22-2200004i−4i−4i4i000000000000000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ1014-4-444-44-444-44-4-44-4-222-2-22-22-22-22-22-220000−4i4i4i−4i0000000000000000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ1024-4-444-4-44-4-44444-4-44-4-444-4-44-4444-44-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-444-4-44-4-44444-4-4-222-2-222-22-2-2-22-222000000000000000000000000000000000000000000000000000023−23−232300000000000000000000
χ1044-4-444-4-44-4-44444-4-4-222-2-222-22-2-2-22-2220000000000000000000000000000000000000000000000000000−232323−2300000000000000000000
χ1054-4-44-4444-444-4-4-4-44-222-22-2-2-22-222-222-24i−4i−4i4i000000000000000000000000−2i2i2i−2i00000000000000000000000000000000000000000000
χ1064-4-44-4444-444-4-4-4-44-222-22-2-2-22-222-222-2−4i4i4i−4i0000000000000000000000002i−2i−2i2i00000000000000000000000000000000000000000000
χ1074-4-44-44-4-44-4-4-44444-222-22-222-222-22-2-2-200000000000000000000004-40000000000000000-22-2200000000000000000000000000000000
χ1084-4-44-44-4-44-4-4-44444-222-22-222-222-22-2-2-20000000000000000000000-4400000000000000002-22-200000000000000000000000000000000

Here i is the imaginary unit (i² = −1).