Finite Group Databasebeta

← Group #10693063

Character table — Group #10693063

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446661212121244466888888881212121212124444121212121212121212122424242424242424224444448888888888242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiii−iii−i−i-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ121111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iii1-1i−i
χ131111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ141111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−ii−i−iii-11i−i
χ151111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−ii−iii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-2220000000022-2-2-2-20000-2-2000000000000000022-2-222-2-2000000000000000000
χ1822222222222-2-22222222-2-2-2220000000022-2-2-2-20000-2-20000000000000000-2-222-2-222000000000000000000
χ192222222-2-2-2-222222-2-2-2-2-2-222200000000-2-2-2-2220000-22000000000000000022-2-2-2-222000000000000000000
χ202222222-2-2-2-222222-2-2-2-2-2-222200000000-2-2-2-2220000-220000000000000000-2-22222-2-2000000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ25222222-1-2-2-2-2-2-2-1-1-1111122-2-1-12i2i2i2i−2i−2i−2i−2i11-1-11122-2-2-11-1-1-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ26222222-1-2-2-2-2-2-2-1-1-1111122-2-1-12i2i2i2i−2i−2i−2i−2i11-1-111-2-222-111111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ27222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i−2i−2i2i2i2i2i11-1-11122-2-2-11-1-1-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ28222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i−2i−2i2i2i2i2i11-1-111-2-222-111111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-2-2222-2-22222222222-2-2-2-222-2-222-2-2-2-222220000-2-20000000022-2-222-2-200000000000000000000000000
χ302222-2-2222-2-22222222222-2-2-2-2-2-222-2-222-2-222220000-2-200000000-2-222-2-22200000000000000000000000000
χ312222-2-2222-2-2-2-22222222-222-2-200000000-2-2-2-2-2-20000220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ322222-2-2222-2-2-2-22222222-222-2-200000000-2-2-2-2-2-2000022000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ332222-2-22-2-22222222-2-2-2-2-22-2-2-20000000022-2-22200002-200000000000000000000000022-2-2-2-2220000000000
χ342222-2-22-2-22222222-2-2-2-2-22-2-2-20000000022-2-22200002-2000000000000000000000000-2-22222-2-20000000000
χ352222-2-22-2-222-2-2222-2-2-2-22-22-2-22i2i−2i−2i−2i−2i2i2i2222-2-20000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-2-222-2-2222-2-2-2-22-22-2-2−2i−2i2i2i2i2i−2i−2i2222-2-20000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-122-2-222-1-1-1-1-1-1-12-2-21122-2-222-2-211-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000000000000000−i3i3−i3i30000
χ382222-2-2-122-2-222-1-1-1-1-1-1-12-2-21122-2-222-2-211-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000
χ392222-2-2-122-2-222-1-1-1-1-1-1-12-2-211-2-222-2-22211-1-1-1-1000011−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000000000000000i3−i3i3−i30000
χ402222-2-2-122-2-222-1-1-1-1-1-1-12-2-211-2-222-2-22211-1-1-1-1000011i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000000000000000−i3i3−i3i30000
χ412222-2-2-1-2-222-2-2-1-1-111112-22112i2i−2i−2i−2i−2i2i2i-1-1-1-11100001-1−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i0000000000000000003−3−330000
χ422222-2-2-1-2-222-2-2-1-1-111112-22112i2i−2i−2i−2i−2i2i2i-1-1-1-11100001-1i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i000000000000000000−333−30000
χ432222-2-2-1-2-222-2-2-1-1-111112-2211−2i−2i2i2i2i2i−2i−2i-1-1-1-11100001-1−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii000000000000000000−333−30000
χ442222-2-2-1-2-222-2-2-1-1-111112-2211−2i−2i2i2i2i2i−2i−2i-1-1-1-11100001-1i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii0000000000000000003−3−330000
χ452-22-22-222i−2i2i−2i00-22-22i2i−2i−2i0002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ462-22-22-222i−2i2i−2i00-22-22i2i−2i−2i0002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ472-22-22-222i−2i2i−2i00-22-22i2i−2i−2i0002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ482-22-22-222i−2i2i−2i00-22-22i2i−2i−2i0002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ492-22-22-22−2i2i−2i2i00-22-2−2i−2i2i2i0002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ502-22-22-22−2i2i−2i2i00-22-2−2i−2i2i2i0002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ512-22-22-22−2i2i−2i2i00-22-2−2i−2i2i2i0002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ522-22-22-22−2i2i−2i2i00-22-2−2i−2i2i2i0002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ532-22-2-2222i−2i−2i2i00-22-22i2i−2i−2i000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i−2i2i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2-2002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000
χ542-22-2-2222i−2i−2i2i00-22-22i2i−2i−2i000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i−2i2i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000
χ552-22-2-2222i−2i−2i2i00-22-22i2i−2i−2i000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2i2i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2-2002i−2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000
χ562-22-2-2222i−2i−2i2i00-22-22i2i−2i−2i000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2i2i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000
χ572-22-2-222−2i2i2i−2i00-22-2−2i−2i2i2i000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i2i−2i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2-200−2i2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000
χ582-22-2-222−2i2i2i−2i00-22-2−2i−2i2i2i000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i2i−2i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i-22002i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000
χ592-22-2-222−2i2i2i−2i00-22-2−2i−2i2i2i000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i2i−2i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2-200−2i2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000
χ602-22-2-222−2i2i2i−2i00-22-2−2i−2i2i2i000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i2i−2i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-22002i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000
χ61444444-24444-4-4-2-2-2-2-2-2-2-4-4-4-2-200000000-2-22222000022000000000000000000000000000000000000000000
χ62444444-2-4-4-4-444-2-2-22222-4-44-2-2000000002222-2-200002-2000000000000000000000000000000000000000000
χ634444-4-4-244-4-4-4-4-2-2-2-2-2-2-2-44422000000002222220000-2-2000000000000000000000000000000000000000000
χ644444-4-4-2-4-44444-2-2-22222-44-42200000000-2-222-2-20000-22000000000000000000000000000000000000000000
χ654-44-44-4-24i−4i4i−4i002-22−2i−2i2i2i000-222+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i−2i2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ664-44-44-4-24i−4i4i−4i002-22−2i−2i2i2i000-22−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i−2i2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ674-44-44-4-2−4i4i−4i4i002-222i2i−2i−2i000-222−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i2i−2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ684-44-44-4-2−4i4i−4i4i002-222i2i−2i−2i000-22−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i2i−2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ694-44-4-44-24i−4i−4i4i002-22−2i−2i2i2i0002-22+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2i−2i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000000000
χ704-44-4-44-24i−4i−4i4i002-22−2i−2i2i2i0002-2−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2i−2i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000000000
χ714-44-4-44-2−4i4i4i−4i002-222i2i−2i−2i0002-22−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i−2i2i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000000000
χ724-44-4-44-2−4i4i4i−4i002-222i2i−2i−2i0002-2−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i−2i2i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000000000
χ734-4-4400400004i−4i-4-440000000000000000000004i−4i2i−2i2-2002i−2i2i−2i2-22-20000000000000000000000000000000000
χ744-4-4400400004i−4i-4-440000000000000000000004i−4i−2i2i-2200−2i2i−2i2i-22-220000000000000000000000000000000000
χ754-4-440040000−4i4i-4-44000000000000000000000−4i4i2i−2i-22002i−2i2i−2i-22-220000000000000000000000000000000000
χ764-4-440040000−4i4i-4-44000000000000000000000−4i4i−2i2i2-200−2i2i−2i2i2-22-20000000000000000000000000000000000
χ774-4-4400-200004i−4i22-223−2323−23000000000000000−2i32i3−2i2i2i−2i2-2002ζ7−2ζ72ζ11−2ζ11−1+i31−i3−1−i31+i30000000000000000000000000000000000
χ784-4-4400-200004i−4i22-223−2323−23000000000000000−2i32i3−2i2i−2i2i-2200−2ζ72ζ7−2ζ112ζ111−i3−1+i31+i3−1−i30000000000000000000000000000000000
χ794-4-4400-200004i−4i22-2−2323−23230000000000000002i3−2i3−2i2i2i−2i2-2002ζ11−2ζ112ζ7−2ζ7−1−i31+i3−1+i31−i30000000000000000000000000000000000
χ804-4-4400-200004i−4i22-2−2323−23230000000000000002i3−2i3−2i2i−2i2i-2200−2ζ112ζ11−2ζ72ζ71+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ814-4-4400-20000−4i4i22-223−2323−230000000000000002i3−2i32i−2i2i−2i-22002ζ11−2ζ112ζ7−2ζ71+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ824-4-4400-20000−4i4i22-223−2323−230000000000000002i3−2i32i−2i−2i2i2-200−2ζ112ζ11−2ζ72ζ7−1−i31+i3−1+i31−i30000000000000000000000000000000000
χ834-4-4400-20000−4i4i22-2−2323−2323000000000000000−2i32i32i−2i2i−2i-22002ζ7−2ζ72ζ11−2ζ111−i3−1+i31+i3−1−i30000000000000000000000000000000000
χ844-4-4400-20000−4i4i22-2−2323−2323000000000000000−2i32i32i−2i−2i2i2-200−2ζ72ζ7−2ζ112ζ11−1+i31−i3−1−i31+i30000000000000000000000000000000000
χ8588-8-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-4000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.