Finite Group Databasebeta

← Group #10691410

Character table — Group #10691410

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424224466668888121212122424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1
χ91-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−iii−i−i11-1-1i−i1-1
χ101-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−i−i−iii-1-111−ii-11
χ111-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii-1-111−i−i−i−iiiiiii−i−i11-1-1−ii-11
χ121-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii-1-111−i−i−i−iiiii−i−iii-1-111i−i1-1
χ131-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii11-1-1−i−i−i−iiiiiii−i−i-1-111i−i-11
χ141-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii−i−iii11-1-1−ii1-1
χ151-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−i-1-111iiii−i−i−i−iii−i−i-1-111−ii1-1
χ161-1-1-111-1111-111-1-11-1-1-1-1-11111111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−i-1-111iiii−i−i−i−i−i−iii11-1-1i−i-11
χ1722222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000022-2-222220000-2-2-2-200000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000-2-222-2-2-2-20000222200000000000000000000
χ19222222222-2-22222-2-2222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ20222222222-2-22222-2-2222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-222-2-2220000000000000000000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-222-2-222000000000000000000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−322-2-2-1-1-1-1000011113−33−33−33−3000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−3-2-22211110000-1-1-1-1−33−33−33−33000000000000
χ2922222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-111-1-111−3−333−3−333−3−333−3−33322-2-2-1-1-1-100001111−33−33−33−33000000000000
χ3022222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-111-1-111−3−333−3−333−3−333−3−333-2-22211110000-1-1-1-13−33−33−33−3000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000−i3i3−i3i30000−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000i3−i3i3−i30000i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000
χ3322222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000−i3i3−i3i30000−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000
χ3422222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000i3−i3i3−i30000i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111220000000011-1-111-1-133−3−333−3−3−3−333−3−3330000−i3i3−i3i32i−2i2i−2ii3−i3i3−i3−i−iii−i−iii000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111220000000011-1-111-1-133−3−333−3−3−3−333−3−3330000i3−i3i3−i3−2i2i−2i2i−i3i3−i3i3ii−i−iii−i−i000000000000
χ3722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111220000000011-1-111-1-1−3−333−3−33333−3−333−3−30000−i3i3−i3i3−2i2i−2i2ii3−i3i3−i3ii−i−iii−i−i000000000000
χ3822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111220000000011-1-111-1-1−3−333−3−33333−3−333−3−30000i3−i3i3−i32i−2i2i−2i−i3i3−i3i3−i−iii−i−iii000000000000
χ39222-2-2-2-222002-22-20022-2-2-2-2222-2-222-2-20000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000−i2i2−i2i22−22−20000
χ40222-2-2-2-222002-22-20022-2-2-2-2222-2-222-2-20000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000i2−i2i2−i2−22−220000
χ41222-2-2-2-222002-22-20022-2-2-2-2222-2-222-2-2000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−i2i2−i2i2−22−220000
χ42222-2-2-2-222002-22-20022-2-2-2-2222-2-222-2-2000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000i2−i2i2−i22−22−20000
χ432-2-22-2-2222002-2-2200-2-222-2-2222-2-2-2-2220000002-2-2200000000000000002-22-2-22-220000000000000000000000002−2−22−222−20000
χ442-2-22-2-2222002-2-2200-2-222-2-2222-2-2-2-2220000002-2-2200000000000000002-22-2-22-22000000000000000000000000−222−22−2−220000
χ452-2-22-2-2222002-2-2200-2-222-2-2222-2-2-2-222000000-222-20000000000000000-22-222-22-20000000000000000000000002−2−222−2−220000
χ462-2-22-2-2222002-2-2200-2-222-2-2222-2-2-2-222000000-222-20000000000000000-22-222-22-2000000000000000000000000−222−2−222−20000
χ472-2-2-222-2222-2-2-2222-2-2-2-2-2222-2-2-2-22222-220000000022-2-2-2-22200000000000000002-2-2222-2-20000-2-22200000000000000000000
χ482-2-2-222-2222-2-2-2222-2-2-2-2-2222-2-2-2-22222-220000000022-2-2-2-2220000000000000000-222-2-2-222000022-2-200000000000000000000
χ492-2-2-222-222-2222-2-2-22-2-2-2-22222222-2-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ502-2-2-222-222-2222-2-2-22-2-2-2-22222222-2-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ512-2-2-222-222-22-2-222-22-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-20000000000000000000000002-2-22000022-2-2-2-222000000000000
χ522-2-2-222-222-22-2-222-22-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-2000000000000000000000000-222-20000-2-22222-2-2000000000000
χ532-2-2-222-22-12-222-2-22-21111-1-1-1-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii2-22-2-1-1112i2i−2i−2i-1-111−i−i−i−iiiii000000000000
χ542-2-2-222-22-12-222-2-22-21111-1-1-1-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-22-2211-1-1−2i−2i2i2i11-1-1iiii−i−i−i−i000000000000
χ552-2-2-222-22-12-222-2-22-21111-1-1-1-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i2-22-2-1-111−2i−2i2i2i-1-111iiii−i−i−i−i000000000000
χ562-2-2-222-22-12-222-2-22-21111-1-1-1-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-22-2211-1-12i2i−2i−2i11-1-1−i−i−i−iiiii000000000000
χ572-2-2-222-22-12-2-2-2222-21111-1-1-11111-1-1-1-1-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-22-1-111000011-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ582-2-2-222-22-12-2-2-2222-21111-1-1-11111-1-1-1-1-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-222-211-1-10000-1-111i3−i3i3−i3−i3i3−i3i3000000000000
χ592-2-2-222-22-12-2-2-2222-21111-1-1-11111-1-1-1-1-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-22-1-111000011-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ602-2-2-222-22-12-2-2-2222-21111-1-1-11111-1-1-1-1-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-222-211-1-10000-1-111−i3i3−i3i3i3−i3i3−i3000000000000
χ612-2-2-222-22-1-2222-2-2-221111-1-1-1-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000−i3i3i3−i30000−i3i3i3−i33−3−33−333−3000000000000
χ622-2-2-222-22-1-2222-2-2-221111-1-1-1-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000i3−i3−i3i30000i3−i3−i3i3−333−33−3−33000000000000
χ632-2-2-222-22-1-2222-2-2-221111-1-1-1-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000−i3i3i3−i30000−i3i3i3−i3−333−33−3−33000000000000
χ642-2-2-222-22-1-2222-2-2-221111-1-1-1-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000i3−i3−i3i30000i3−i3−i3i33−3−33−333−3000000000000
χ652-2-2-222-22-1-22-2-222-221111-1-1-11111-1-1-1-12-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−i3i3i3−i32-2-22i3−i3−i3i3-1-11111-1-1000000000000
χ662-2-2-222-22-1-22-2-222-221111-1-1-11111-1-1-1-12-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000i3−i3−i3i3-222-2−i3i3i3−i311-1-1-1-111000000000000
χ672-2-2-222-22-1-22-2-222-221111-1-1-11111-1-1-1-12-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−i3i3i3−i3-222-2i3−i3−i3i311-1-1-1-111000000000000
χ682-2-2-222-22-1-22-2-222-221111-1-1-11111-1-1-1-12-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000i3−i3−i3i32-2-22−i3i3i3−i3-1-11111-1-1000000000000
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χ71444-4-4-4-44-2004-44-400-2-22222-2-2-222-2-222000000−4i4i−4i4i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
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χ7444-444-4-4-44000000004-44-44-4-4000000000022−2222−2200000000000022−2222−2222−2222−2200000000000000000000000000000000000000000000
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χ7744-444-4-4-4-200000000-22-22-22223−2323−2323−2323−2300−2222−2222000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000000000
χ7844-444-4-4-4-200000000-22-22-222−2323−2323−2323−23230022−2222−220000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000
χ7944-444-4-4-4-200000000-22-22-222−2323−2323−2323−232300−2222−2222000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000000
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χ864-444-44-4-444-40000-44-444-4-44-40000000000000000004-400-44000000000000000000000000000000000000000000000000000000
χ874-444-44-4-44-4400004-4-444-4-44-4000000000000000000-44004-4000000000000000000000000000000000000000000000000000000
χ884-444-44-4-4-24-40000-442-2-222-2223−23−2323−232323−230000000000-2223−232-2−23230000000000000000000000000000000000000000000000000000
χ894-444-44-4-4-24-40000-442-2-222-22−232323−2323−23−23230000000000-22−23232-223−230000000000000000000000000000000000000000000000000000
χ904-444-44-4-4-2-4400004-42-2-222-2223−23−2323−232323−2300000000002-2−2323-2223−230000000000000000000000000000000000000000000000000000
χ914-444-44-4-4-2-4400004-42-2-222-22−232323−2323−23−232300000000002-223−23-22−23230000000000000000000000000000000000000000000000000000
χ924-44-44-44-4400000000-44-444-4-40000000000−2i22i22i2−2i2000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ934-44-44-44-4400000000-44-444-4-400000000002i2−2i2−2i22i20000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ944-44-44-44-4-2000000002-22-2-22223−2323−23−2323−232300−2i22i22i2−2i20000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000000000
χ954-44-44-44-4-2000000002-22-2-22223−2323−23−2323−2323002i2−2i2−2i22i2000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000000000
χ964-44-44-44-4-2000000002-22-2-222−2323−232323−2323−2300−2i22i22i2−2i20000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000000000
χ974-44-44-44-4-2000000002-22-2-222−2323−232323−2323−23002i2−2i2−2i22i2000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000000000
χ984-4-44-4-444400-444-400-4-444-4-44-4-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-44-4-444-2004-4-440022-2-222-2-2-22222-2-20000004-4-440000000000000000-22-222-22-2000000000000000000000000000000000000
χ1004-4-44-4-444-2004-4-440022-2-222-2-2-22222-2-2000000-444-400000000000000002-22-2-22-22000000000000000000000000000000000000
χ1014-4-44-4-444-200-444-40022-2-222-222-2-2-2-2220000000000000000000000000023−23−2323−232323−23000000000000000000000000000000000000
χ1024-4-44-4-444-200-444-40022-2-222-222-2-2-2-22200000000000000000000000000−232323−2323−23−2323000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.