Finite Group Databasebeta

← Group #10733228

Character table — Group #10733228

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111111122222222222222224444444488888888888888888888888888888888888888121212121212121212121212121212122424242424242424
order1222222222222222366666666666666644444444444444444412121212121212121212121212121212121212121212121212121212222244444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111-1-1-1-11111000000000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-222-2-222-2-2-1-1-1-11111-1-1-1-1111111111111-1-1-1-1000000000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-222-2-222-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-11111-1-1-1-111111111000000000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-111111111-1-1-1-1000000000000000000000000
χ252222-2-222-2-22-2-2-2-2222222-2-2-2-2-2222-2-2-200002i2i−2i−2i0000000000000000000000000000002i2i−2i−2i000000002i2i−2i−2i0000000000002-200
χ262222-2-222-2-22-2-2-2-2222222-2-2-2-2-2222-2-2-200002i2i−2i−2i0000000000000000000000000000002i2i−2i−2i00000000−2i−2i2i2i000000000000-2200
χ272222-2-222-2-22-2-2-2-2222222-2-2-2-2-2222-2-2-20000−2i−2i2i2i000000000000000000000000000000−2i−2i2i2i000000002i2i−2i−2i000000000000-2200
χ282222-2-222-2-22-2-2-2-2222222-2-2-2-2-2222-2-2-20000−2i−2i2i2i000000000000000000000000000000−2i−2i2i2i00000000−2i−2i2i2i0000000000002-200
χ29222-22-22-2-2-2-222-22-2222-2-2222-2-22-2-2-2-2200000000002i−2i000000000000002i2i−2i−2i000000000000000022-2-2000000002i2i−2i−2i00000000
χ30222-22-22-2-2-2-222-22-2222-2-2222-2-22-2-2-2-2200000000002i−2i000000000000002i2i−2i−2i0000000000000000-2-22200000000−2i−2i2i2i00000000
χ31222-22-22-2-2-2-222-22-2222-2-2222-2-22-2-2-2-220000000000−2i2i00000000000000−2i−2i2i2i000000000000000022-2-200000000−2i−2i2i2i00000000
χ32222-22-22-2-2-2-222-22-2222-2-2222-2-22-2-2-2-220000000000−2i2i00000000000000−2i−2i2i2i0000000000000000-2-222000000002i2i−2i−2i00000000
χ3322-22-22-22-2-2-22-222-222-22-22-2-222-22-2-2-222i2i−2i−2i000000000000002i2i−2i−2i0000000000000000000000002-22-20000000000000000002i−2i
χ3422-22-22-22-2-2-22-222-222-22-22-2-222-22-2-2-222i2i−2i−2i000000000000002i2i−2i−2i000000000000000000000000-22-22000000000000000000−2i2i
χ3522-22-22-22-2-2-22-222-222-22-22-2-222-22-2-2-22−2i−2i2i2i00000000000000−2i−2i2i2i0000000000000000000000002-22-2000000000000000000−2i2i
χ3622-22-22-22-2-2-22-222-222-22-22-2-222-22-2-2-22−2i−2i2i2i00000000000000−2i−2i2i2i000000000000000000000000-22-220000000000000000002i−2i
χ3722-2-222-2-2-2-22-222-2222-2-22-22222-2-22-2-2-200000000000000002-2000000000000000022-2-20000000000002i−2i2i−2i2i2i−2i−2i000000000000
χ3822-2-222-2-2-2-22-222-2222-2-22-22222-2-22-2-2-200000000000000002-2000000000000000022-2-2000000000000−2i2i−2i2i−2i−2i2i2i000000000000
χ3922-2-222-2-2-2-22-222-2222-2-22-22222-2-22-2-2-20000000000000000-220000000000000000-2-2220000000000002i−2i2i−2i−2i−2i2i2i000000000000
χ4022-2-222-2-2-2-22-222-2222-2-22-22222-2-22-2-2-20000000000000000-220000000000000000-2-222000000000000−2i2i−2i2i2i2i−2i−2i000000000000
χ4122-2-2-2-2-2-22222-2-22222-2-222-2-2-2-2-2-22222000000000000002-20000000000000000000000000022-2-22-2-222-2-220000000000000000
χ4222-2-2-2-2-2-22222-2-22222-2-222-2-2-2-2-2-22222000000000000002-20000000000000000000000000022-2-2-222-2-222-20000000000000000
χ4322-2-2-2-2-2-22222-2-22222-2-222-2-2-2-2-2-2222200000000000000-2200000000000000000000000000-2-2222-2-22-222-20000000000000000
χ4422-2-2-2-2-2-22222-2-22222-2-222-2-2-2-2-2-2222200000000000000-2200000000000000000000000000-2-222-222-22-2-220000000000000000
χ452-222-22-2-22-22-22-22-22-2222-22-22-2-2-2-22-220000000000002i−2i00000000000000002i2i−2i−2i000000000000000000002-22-22i−2i2i−2i00000000
χ462-222-22-2-22-22-22-22-22-2222-22-22-2-2-2-22-220000000000002i−2i00000000000000002i2i−2i−2i00000000000000000000-22-22−2i2i−2i2i00000000
χ472-222-22-2-22-22-22-22-22-2222-22-22-2-2-2-22-22000000000000−2i2i0000000000000000−2i−2i2i2i000000000000000000002-22-2−2i2i−2i2i00000000
χ482-222-22-2-22-22-22-22-22-2222-22-22-2-2-2-22-22000000000000−2i2i0000000000000000−2i−2i2i2i00000000000000000000-22-222i−2i2i−2i00000000
χ492-22-222-222-2-22-2-2-222-22-2-22-222-2-2222-2-22-22-22i−2i2i−2i2i−2i000000002-22-22i2i−2i−2i0000000000002i−2i2i−2i0000000000000000000000000000
χ502-22-222-222-2-22-2-2-222-22-2-22-222-2-2222-2-22-22-2−2i2i−2i2i−2i2i000000002-22-2−2i−2i2i2i000000000000−2i2i−2i2i0000000000000000000000000000
χ512-22-222-222-2-22-2-2-222-22-2-22-222-2-2222-2-2-22-222i−2i2i−2i−2i2i00000000-22-22−2i−2i2i2i0000000000002i−2i2i−2i0000000000000000000000000000
χ522-22-222-222-2-22-2-2-222-22-2-22-222-2-2222-2-2-22-22−2i2i−2i2i2i−2i00000000-22-222i2i−2i−2i000000000000−2i2i−2i2i0000000000000000000000000000
χ532-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-1112-22-22i−2i2i−2i2i−2i00000000-11-11−i−iii3−33−3−i3i3−i3i3−i3i3−i3i3−ii−ii3−33−3000000000000000000000000
χ542-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-1112-22-22i−2i2i−2i2i−2i00000000-11-11−i−iii−33−33i3−i3i3−i3i3−i3i3−i3−ii−ii−33−33000000000000000000000000
χ552-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-1112-22-2−2i2i−2i2i−2i2i00000000-11-11ii−i−i3−33−3i3−i3i3−i3i3−i3i3−i3i−ii−i3−33−3000000000000000000000000
χ562-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-1112-22-2−2i2i−2i2i−2i2i00000000-11-11ii−i−i−33−33−i3i3−i3i3−i3i3−i3i3i−ii−i−33−33000000000000000000000000
χ572-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-111-22-222i−2i2i−2i−2i2i000000001-11-1ii−i−i3−33−3−i3i3−i3i3i3−i3i3−i3−ii−ii−33−33000000000000000000000000
χ582-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-111-22-222i−2i2i−2i−2i2i000000001-11-1ii−i−i−33−33i3−i3i3−i3−i3i3−i3i3−ii−ii3−33−3000000000000000000000000
χ592-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-111-22-22−2i2i−2i2i2i−2i000000001-11-1−i−iii3−33−3i3−i3i3−i3−i3i3−i3i3i−ii−i−33−33000000000000000000000000
χ602-22-222-222-2-22-2-2-22-11-111-11-1-111-1-1-111-22-22−2i2i−2i2i2i−2i000000001-11-1−i−iii−33−33−i3i3−i3i3i3−i3i3−i3i−ii−i3−33−3000000000000000000000000
χ612-22-2-2-2-22-22-2-222222-22-2-2-22-2-22-222-22200002-2-220000000000000000000000000000002-2-2200000000000000002-2-22002-20000
χ622-22-2-2-2-22-22-2-222222-22-2-2-22-2-22-222-22200002-2-220000000000000000000000000000002-2-220000000000000000-222-200-220000
χ632-22-2-2-2-22-22-2-222222-22-2-2-22-2-22-222-2220000-222-2000000000000000000000000000000-222-200000000000000002-2-2200-220000
χ642-22-2-2-2-22-22-2-222222-22-2-2-22-2-22-222-2220000-222-2000000000000000000000000000000-222-20000000000000000-222-2002-20000
χ652-2-2-2-2222-22222-2-2-22-2-2-2222-22-222-2-22-22i−2i−2i2i000000000000002i−2i−2i2i000000000000000000000000000000002i−2i−2i2i00002-2000000
χ662-2-2-2-2222-22222-2-2-22-2-2-2222-22-222-2-22-22i−2i−2i2i000000000000002i−2i−2i2i00000000000000000000000000000000−2i2i2i−2i0000-22000000
χ672-2-2-2-2222-22222-2-2-22-2-2-2222-22-222-2-22-2−2i2i2i−2i00000000000000−2i2i2i−2i000000000000000000000000000000002i−2i−2i2i0000-22000000
χ682-2-2-2-2222-22222-2-2-22-2-2-2222-22-222-2-22-2−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i00002-2000000
χ694444-4-444-4-44-4-4-4-44-2-2-2-2-222222-2-2-222200004i4i−4i−4i000000000000000000000000000000−2i−2i2i2i0000000000000000000000000000
χ704444-4-444-4-44-4-4-4-44-2-2-2-2-222222-2-2-22220000−4i−4i4i4i0000000000000000000000000000002i2i−2i−2i0000000000000000000000000000
χ71444-44-44-4-4-4-444-44-4-2-2-222-2-2-222-22222-200000000004i−4i00000000000000−2i−2i2i2i0000000000000000000000000000000000000000
χ72444-44-44-4-4-4-444-44-4-2-2-222-2-2-222-22222-20000000000−4i4i000000000000002i2i−2i−2i0000000000000000000000000000000000000000
χ73444-4-444-444-4-4-44-4-4444-4-4-4-4-4444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-444-444-4-4-44-4-4-2-2-222222-2-2-222-2-2200000000000000000000000000000023−23−2323000000000000000000000000000000000000
χ75444-4-444-444-4-4-44-4-4-2-2-222222-2-2-222-2-22000000000000000000000000000000−232323−23000000000000000000000000000000000000
χ7644-444-4-4444-4-44-4-4-444-44-4-444-4-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ7744-444-4-4444-4-44-4-4-4-2-22-222-2-2222-22-2-22000000000000000000000023−2323−2300000000000000000000000000000000000000000000
χ7844-444-4-4444-4-44-4-4-4-2-22-222-2-2222-22-2-220000000000000000000000−2323−232300000000000000000000000000000000000000000000
χ7944-44-44-44-4-4-44-444-4-2-22-22-222-2-22-2222-24i4i−4i−4i00000000000000−2i−2i2i2i000000000000000000000000000000000000000000000000
χ8044-44-44-44-4-4-44-444-4-2-22-22-222-2-22-2222-2−4i−4i4i4i000000000000002i2i−2i−2i000000000000000000000000000000000000000000000000
χ8144-4-444-4-4-4-44-444-44-2-222-22-2-2-2-222-222200000000000000004-40000000000000000-2-22200000000000000000000000000000000
χ8244-4-444-4-4-4-44-444-44-2-222-22-2-2-2-222-22220000000000000000-44000000000000000022-2-200000000000000000000000000000000
χ8344-4-4-4-4-4-44444-4-444-2-222-2-2222222-2-2-2-2000000000000004-400000000000000000000000000-2-222000000000000000000000000
χ8444-4-4-4-4-4-44444-4-444-2-222-2-2222222-2-2-2-200000000000000-440000000000000000000000000022-2-2000000000000000000000000
χ854-4444-4-4-4-4444-44-4-44-44444-44-44-4-4-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ864-4444-4-4-4-4444-44-4-4-22-2-2-2-22-22-22222-2200000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ874-4444-4-4-4-4444-44-4-4-22-2-2-2-22-22-22222-22000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ884-444-44-4-44-44-44-44-4-22-2-2-22-22-22222-22-20000000000004i−4i0000000000000000−2i−2i2i2i000000000000000000000000000000000000
χ894-444-44-4-44-44-44-44-4-22-2-2-22-22-22222-22-2000000000000−4i4i00000000000000002i2i−2i−2i000000000000000000000000000000000000
χ904-44-4-4-4-44-44-4-44444-22-2222-222-22-2-22-2-200004-4-44000000000000000000000000000000-222-20000000000000000000000000000
χ914-44-4-4-4-44-44-4-44444-22-2222-222-22-2-22-2-20000-444-40000000000000000000000000000002-2-220000000000000000000000000000
χ924-4-44444-4-44-4-4-4-4444-4-44-4-4-444-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-44444-4-44-4-4-4-444-222-2222-2-22-22-22-2-20000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ944-4-44444-4-44-4-4-4-444-222-2222-2-22-22-22-2-200000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ954-4-44-4-44-44-4-4444-444-4-44-444-4-444-444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ964-4-44-4-44-44-4-4444-44-222-22-2-222-2-22-2-22200000000000000000000000000000000000000000023−23−2323000000000000000000000000
χ974-4-44-4-44-44-4-4444-44-222-22-2-222-2-22-2-222000000000000000000000000000000000000000000−232323−23000000000000000000000000
χ984-4-4-44-4444-44-4-444-44-4-4-44-4-44-4444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-4-44-4444-44-4-444-4-2222-222-22-2-2-22-22-20000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ1004-4-4-44-4444-44-4-444-4-2222-222-22-2-2-22-22-200000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ1014-4-4-4-4444-44444-4-4-4-2222-2-2-22-22-2-222-224i−4i−4i4i00000000000000−2i2i2i−2i000000000000000000000000000000000000000000000000
χ1024-4-4-4-4444-44444-4-4-4-2222-2-2-22-22-2-222-22−4i4i4i−4i000000000000002i−2i−2i2i000000000000000000000000000000000000000000000000

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