Finite Group Databasebeta

← Group #10703020

Character table — Group #10703020

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222222223444444446666666666612121212121212122244444466668888121212121212121212121212242424242424242488888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
χ1011-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii
χ1111-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ1211-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ1311-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-11-11-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iii−i−i−i−iii−i−iii
χ1411-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-11-11-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ1511-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-11-11-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ1611-1-1-111-111-1-11111-11-1-1-11-1-1-1-11111-1-1111-1-1-1-11-11-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2322222222-2-2-2-2222-2-2-222-22222222-2-2-2-222-222-2-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-2-2-2222-2-2-222-22222222-2-2-2-222-222-2-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-2-2-22-2-2222-2-222222222-2-2-2-2-2-22-2-222222-2-2000022220000-2-2-2-2000000000000000000000000000000000000
χ2622222222-2-2-2-22-2-2222-2-222222222-2-2-2-2-2-22-2-2222-2-2220000-2-2-2-200002222000000000000000000000000000000000000
χ2722222222-2-2-2-2-1-2-2222-2-22-1-1-1-1-1-1-1111111-111-1-1-122-2-20000-1-1-1-100001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2822222222-2-2-2-2-1-2-2222-2-22-1-1-1-1-1-1-1111111-111-1-1-122-2-20000-1-1-1-100001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2922222222-2-2-2-2-1-2-2222-2-22-1-1-1-1-1-1-1111111-111-1-1-1-2-222000011110000-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3022222222-2-2-2-2-1-2-2222-2-22-1-1-1-1-1-1-1111111-111-1-1-1-2-222000011110000-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ3122-2-2-222-222-2-22-2-2-22-22222-2-2-2-22222-2-2-2-2-22222-20000000000000000000000000000000000000000000000002-2-220000
χ3222-2-2-222-222-2-22-2-2-22-22222-2-2-2-22222-2-2-2-2-22222-2000000000000000000000000000000000000000000000000-222-20000
χ3322-2-2-222-222-2-2-1222-22-2-2-2-11111-1-1-1-111-1-1-11111-12-22-222-2-2-1-11122-2-2-1-111-1-1-1-11111-1-1-1-1111100000000000000000000
χ3422-2-2-222-222-2-2-1222-22-2-2-2-11111-1-1-1-111-1-1-11111-12-22-2-2-222-1-111-2-222-1-1111111-1-1-1-11111-1-1-1-100000000000000000000
χ3522-2-2-222-222-2-2-1222-22-2-2-2-11111-1-1-1-111-1-1-11111-1-22-2222-2-211-1-1-2-22211-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ3622-2-2-222-222-2-2-1222-22-2-2-2-11111-1-1-1-111-1-1-11111-1-22-22-2-22211-1-122-2-211-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ3722-2-2-222-2-2-222222-22-2-2-222-2-2-2-222-2-22222-2-2-222-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ3822-2-2-222-2-2-222222-22-2-2-222-2-2-2-222-2-22222-2-2-222-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ3922-2-2-222-2-2-2222-2-22-2222-22-2-2-2-222-2-222-2-2222-2-222-2-22000022-2-20000-2-222000000000000000000000000000000000000
χ4022-2-2-222-2-2-2222-2-22-2222-22-2-2-2-222-2-222-2-2222-2-22-222-20000-2-222000022-2-2000000000000000000000000000000000000
χ4122-2-2-222-2-2-222-1-2-22-2222-2-11111-1-111-1-111-1-1-111-12-2-220000-1-111000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4222-2-2-222-2-2-222-1-2-22-2222-2-11111-1-111-1-111-1-1-111-12-2-220000-1-111000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ4322-2-2-222-2-2-222-1-2-22-2222-2-11111-1-111-1-111-1-1-111-1-222-2000011-1-10000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ4422-2-2-222-2-2-222-1-2-22-2222-2-11111-1-111-1-111-1-1-111-1-222-2000011-1-10000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ452-222-22-2-22-22-222-22-2-22-22-222-2-22-22-22-22-222-22-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-222-22-2-22-22-222-22-2-22-22-222-2-22-22-22-22-222-22-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-222-22-2-22-22-22-22-222-22-2-222-2-22-22-22-2-22-2-22-222000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ482-222-22-2-22-22-22-22-222-22-2-222-2-22-22-22-2-22-2-22-22200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ492-222-22-2-22-22-2-12-22-2-22-221-1-111-11-11-11-11-1-11-11100000000−i3i3−i3i32i−2i2i−2i−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii00000000000000000000
χ502-222-22-2-22-22-2-12-22-2-22-221-1-111-11-11-11-11-1-11-11100000000−i3i3−i3i3−2i2i−2i2i−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i00000000000000000000
χ512-222-22-2-22-22-2-12-22-2-22-221-1-111-11-11-11-11-1-11-11100000000i3−i3i3−i32i−2i2i−2ii3−i3i3−i3−33−33−33−33−ii−ii−ii−ii00000000000000000000
χ522-222-22-2-22-22-2-12-22-2-22-221-1-111-11-11-11-11-1-11-11100000000i3−i3i3−i3−2i2i−2i2ii3−i3i3−i33−33−33−33−3i−ii−ii−ii−i00000000000000000000
χ532-222-22-2-2-22-2222-2-2222-2-2-222-2-22-2-22-222-2-22-2-22200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ542-222-22-2-2-22-2222-2-2222-2-2-222-2-22-2-22-222-2-22-2-2220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ552-222-22-2-2-22-222-222-2-2-222-222-2-22-2-22-22-222-222-2-200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ562-222-22-2-2-22-222-222-2-2-222-222-2-22-2-22-22-222-222-2-20000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ572-222-22-2-2-22-22-1-222-2-2-2221-1-111-111-11-11-1-11-1-11100002i−2i2i−2i−i3i3−i3i30000i3−i3i3−i3−iii−i−iii−i3−3−333−3−3300000000000000000000
χ582-222-22-2-2-22-22-1-222-2-2-2221-1-111-111-11-11-1-11-1-11100002i−2i2i−2ii3−i3i3−i30000−i3i3−i3i3−iii−i−iii−i−333−3−333−300000000000000000000
χ592-222-22-2-2-22-22-1-222-2-2-2221-1-111-111-11-11-1-11-1-1110000−2i2i−2i2i−i3i3−i3i30000i3−i3i3−i3i−i−iii−i−ii−333−3−333−300000000000000000000
χ602-222-22-2-2-22-22-1-222-2-2-2221-1-111-111-11-11-1-11-1-1110000−2i2i−2i2ii3−i3i3−i30000−i3i3−i3i3i−i−iii−i−ii3−3−333−3−3300000000000000000000
χ612-2-2-222-222-2-2222-222-2-22-2-2-2-2222-22-2-222-22-22-22-20000000000002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ622-2-2-222-222-2-2222-222-2-22-2-2-2-2222-22-2-222-22-22-22-2000000000000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ632-2-2-222-222-2-222-22-2-222-22-2-2-2222-22-2-22-22-22-22-22000000000000000000000000000000000000000000002-2-2200000000
χ642-2-2-222-222-2-222-22-2-222-22-2-2-2222-22-2-22-22-22-22-2200000000000000000000000000000000000000000000-222-200000000
χ652-2-2-222-222-2-22-12-222-2-22-2111-1-1-11-111-1-11-11-11-1100000000−i3i3i3−i32i−2i−2i2i−i3i3i3−i33−33−3−33−33−ii−iii−ii−i00000000000000000000
χ662-2-2-222-222-2-22-12-222-2-22-2111-1-1-11-111-1-11-11-11-1100000000−i3i3i3−i3−2i2i2i−2i−i3i3i3−i3−33−333−33−3i−ii−i−ii−ii00000000000000000000
χ672-2-2-222-222-2-22-12-222-2-22-2111-1-1-11-111-1-11-11-11-1100000000i3−i3−i3i32i−2i−2i2ii3−i3−i3i3−33−333−33−3−ii−iii−ii−i00000000000000000000
χ682-2-2-222-222-2-22-12-222-2-22-2111-1-1-11-111-1-11-11-11-1100000000i3−i3−i3i3−2i2i2i−2ii3−i3−i3i33−33−3−33−33i−ii−i−ii−ii00000000000000000000
χ692-2-2-222-22-222-222-2-2-22-222-2-2-2222-2-222-22-2-2-222-2200000000000000000000000000000000000000000000000000002-2-22
χ702-2-2-222-22-222-222-2-2-22-222-2-2-2222-2-222-22-2-2-222-220000000000000000000000000000000000000000000000000000-222-2
χ712-2-2-222-22-222-22-2222-22-2-2-2-2-2222-2-222-2-2222-2-22-200002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ722-2-2-222-22-222-22-2222-22-2-2-2-2-2222-2-222-2-2222-2-22-20000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ732-2-2-222-22-222-2-1-2222-22-2-2111-1-1-111-1-111-1-1-111-1100002i−2i−2i2i−i3i3i3−i30000i3−i3−i3i3−iii−ii−i−ii3−3−33−333−300000000000000000000
χ742-2-2-222-22-222-2-1-2222-22-2-2111-1-1-111-1-111-1-1-111-1100002i−2i−2i2ii3−i3−i3i30000−i3i3i3−i3−iii−ii−i−ii−333−33−3−3300000000000000000000
χ752-2-2-222-22-222-2-1-2222-22-2-2111-1-1-111-1-111-1-1-111-110000−2i2i2i−2i−i3i3i3−i30000i3−i3−i3i3i−i−ii−iii−i−333−33−3−3300000000000000000000
χ762-2-2-222-22-222-2-1-2222-22-2-2111-1-1-111-1-111-1-1-111-110000−2i2i2i−2ii3−i3−i3i30000−i3i3i3−i3i−i−ii−iii−i3−3−33−333−300000000000000000000
χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-244-4-4-444-4-2-2-2-2-2-2-22222-2-22-2-222200000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-4000040000000044-44-4-4-40000000000000000000000000000000000000000000000000022−220022−22000000000000
χ80444-44-4-4-4000040000000044-44-4-4-400000000000000000000000000000000000000000000000000−222200−2222000000000000
χ8144-44-4-4-4400004000000004-44-44-4-400000000000000000000000000000000000000000000000000−2i22i2002i2−2i2000000000000
χ8244-44-4-4-4400004000000004-44-44-4-4000000000000000000000000000000000000000000000000002i2−2i200−2i22i2000000000000
χ8344-4-4-444-444-4-4-2-4-4-44-4444-22222-2-2-2-222222-2-2-2-2200000000000000000000000000000000000000000000000000000000
χ8444-4-4-444-4-4-444-244-44-4-4-44-22222-2-222-2-2-2-2222-2-2200000000000000000000000000000000000000000000000000000000
χ854-444-44-4-44-44-4-2-44-444-44-42-2-222-22-22-222-222-22-2-200000000000000000000000000000000000000000000000000000000
χ864-444-44-4-4-44-44-24-4-4444-4-42-2-222-222-22-2-222-222-2-200000000000000000000000000000000000000000000000000000000
χ874-44-4-4-4440000400000000-44-4-44-4400000000000000000000000000000000000000000000000022−220022−2200000000000000
χ884-44-4-4-4440000400000000-44-4-44-44000000000000000000000000000000000000000000000000−222200−222200000000000000
χ894-4-444-44-40000400000000-4-444-4-44000000000000000000000000000000000000000000000000−2i22i2002i2−2i200000000000000
χ904-4-444-44-40000400000000-4-444-4-440000000000000000000000000000000000000000000000002i2−2i200−2i22i200000000000000
χ914-4-4-444-444-4-44-2-44-4-444-44222-2-2-22-222-22-22-22-22-200000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-444-4-24-4-4-44-444222-2-2-222-2-22-2222-2-22-200000000000000000000000000000000000000000000000000000000
χ93888-88-8-8-80000-400000000-4-44-444400000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-8-8-880000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-8-8880000-4000000004-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-88-80000-40000000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000

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