Finite Group Databasebeta

← Group #10690809

Character table — Group #10690809

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424242244444444121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111-1-1ii−i−iii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-111-1-1−i−iii−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-1-111ii−i−i−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-1-111−i−iiiii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-1-111−i−iiiii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11-1-111ii−i−i−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-111-1-1−i−iii−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-111-1-1ii−i−iii−i−i-11
χ1722222222222-2-2-2-2222222222-2-222-2-222-2-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2222222222-2-222-2-222-2-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-22222-2-22222222-2-2-2-222-2-22200000000-2-2000000000000000022-2-2-2-2220000000000000000
χ20222222222-2-22222-2-22222222-2-2-2-222-2-22200000000-2-20000000000000000-2-22222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i2i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ2922-2-222-2-222i−2i00002i−2i22-2-2-22-2002i−2i002i−2i001+i−1−i1−i−1+i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000002-2002i−2i000000001+i−1−i1−i−1+i000000
χ3022-2-222-2-222i−2i00002i−2i22-2-2-22-2002i−2i002i−2i001+i−1−i1−i−1+i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000-2200−2i2i00000000−1−i1+i−1+i1−i000000
χ3122-2-222-2-222i−2i00002i−2i22-2-2-22-2002i−2i002i−2i00−1−i1+i−1+i1−i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002-2002i−2i00000000−1−i1+i−1+i1−i000000
χ3222-2-222-2-222i−2i00002i−2i22-2-2-22-2002i−2i002i−2i00−1−i1+i−1+i1−i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000-2200−2i2i000000001+i−1−i1−i−1+i000000
χ3322-2-222-2-22−2i2i0000−2i2i22-2-2-22-200−2i2i00−2i2i001−i−1+i1+i−1−i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002-200−2i2i000000001−i−1+i1+i−1−i000000
χ3422-2-222-2-22−2i2i0000−2i2i22-2-2-22-200−2i2i00−2i2i001−i−1+i1+i−1−i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000-22002i−2i00000000−1+i1−i−1−i1+i000000
χ3522-2-222-2-22−2i2i0000−2i2i22-2-2-22-200−2i2i00−2i2i00−1+i1−i−1−i1+i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002-200−2i2i00000000−1+i1−i−1−i1+i000000
χ3622-2-222-2-22−2i2i0000−2i2i22-2-2-22-200−2i2i00−2i2i00−1+i1−i−1−i1+i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000-22002i−2i000000001−i−1+i1+i−1−i000000
χ372-2-222-22-222222-2-2-2-2-2-2-2-22222-222-2-2-2-222000000002-200000000000000000000000000000000002i−2i2i−2i00
χ382-2-222-22-222222-2-2-2-2-2-2-2-22222-222-2-2-2-222000000002-20000000000000000000000000000000000−2i2i−2i2i00
χ392-2-222-22-2222-2-222-2-2-2-2-2-2222-222222-2-2-2-200002i−2i2i−2i-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ402-2-222-22-2222-2-222-2-2-2-2-2-2222-222222-2-2-2-20000−2i2i−2i2i-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ412-2-222-22-22-2-222-2-222-2-2-2-2222-22-2-2-2-2222200002-2-22-220000000022-2-2-2-222000000000000000000000000
χ422-2-222-22-22-2-222-2-222-2-2-2-2222-22-2-2-2-222220000-222-2-2200000000-2-22222-2-2000000000000000000000000
χ432-2-222-22-22-2-2-2-22222-2-2-2-22222-2-2-22222-2-2000000002-200000000000000000000000000000000002-2-2200
χ442-2-222-22-22-2-2-2-22222-2-2-2-22222-2-2-22222-2-2000000002-20000000000000000000000000000000000-222-200
χ452-2-222-22-2-122-2-222-2-21111-1-1-1-22-1-1-1-1111100002i−2i2i−2i1-13−33−33−33−3−i−iii−i−iii0000000000−i3i3−i3i30000000000
χ462-2-222-22-2-122-2-222-2-21111-1-1-1-22-1-1-1-1111100002i−2i2i−2i1-1−33−33−33−33−i−iii−i−iii0000000000i3−i3i3−i30000000000
χ472-2-222-22-2-122-2-222-2-21111-1-1-1-22-1-1-1-111110000−2i2i−2i2i1-13−33−33−33−3ii−i−iii−i−i0000000000i3−i3i3−i30000000000
χ482-2-222-22-2-122-2-222-2-21111-1-1-1-22-1-1-1-111110000−2i2i−2i2i1-1−33−33−33−33ii−i−iii−i−i0000000000−i3i3−i3i30000000000
χ492-2-222-22-2-1-2-222-2-2221111-1-1-1-221111-1-1-1-100002-2-221-1−i3i3−i3i3i3−i3i3−i3-1-11111-1-10000000000−i3i3i3−i30000000000
χ502-2-222-22-2-1-2-222-2-2221111-1-1-1-221111-1-1-1-100002-2-221-1i3−i3i3−i3−i3i3−i3i3-1-11111-1-10000000000i3−i3−i3i30000000000
χ512-2-222-22-2-1-2-222-2-2221111-1-1-1-221111-1-1-1-10000-222-21-1−i3i3−i3i3i3−i3i3−i311-1-1-1-1110000000000i3−i3−i3i30000000000
χ522-2-222-22-2-1-2-222-2-2221111-1-1-1-221111-1-1-1-10000-222-21-1i3−i3i3−i3−i3i3−i3i311-1-1-1-1110000000000−i3i3i3−i30000000000
χ5344444444-244-4-4-4-444-2-2-2-2-2-2-2-4-4-2-222-2-22200000000220000000000000000000000000000000000000000
χ5444444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-222-2-200000000220000000000000000000000000000000000000000
χ554444-4-4-4-44000000004-44-44-4-4000000000000000000000000000000000000004-400000000000000000000
χ564444-4-4-4-44000000004-44-44-4-400000000000000000000000000000000000000-4400000000000000000000
χ5744-4-444-4-4-24i−4i00004i−4i-2-2222-2200−2i2i00−2i2i002+2i−2−2i2−2i−2+2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000000000
χ5844-4-444-4-4-24i−4i00004i−4i-2-2222-2200−2i2i00−2i2i00−2−2i2+2i−2+2i2−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000000000
χ5944-4-444-4-4-2−4i4i0000−4i4i-2-2222-22002i−2i002i−2i002−2i−2+2i2+2i−2−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000000000
χ6044-4-444-4-4-2−4i4i0000−4i4i-2-2222-22002i−2i002i−2i00−2+2i2−2i−2−2i2+2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000000000000000
χ6144-4-4-4-4444004i−4i4i−4i004-4-44-4-4400004i−4i004i−4i00000000000000000000000000000000000000000000000000
χ6244-4-4-4-444400−4i4i−4i4i004-4-44-4-440000−4i4i00−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-2004i−4i4i−4i00-222-222-20000−2i2i00−2i2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000000
χ6444-4-4-4-444-2004i−4i4i−4i00-222-222-20000−2i2i00−2i2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000000
χ6544-4-4-4-444-200−4i4i−4i4i00-222-222-200002i−2i002i−2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000000
χ6644-4-4-4-444-200−4i4i−4i4i00-222-222-200002i−2i002i−2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000000
χ674-44-44-4-4444i−4i0000−4i4i-4-444-44-4004i−4i00−4i4i0000000000000000000000000000000000000000000000000000
χ684-44-44-4-444−4i4i00004i−4i-4-444-44-400−4i4i004i−4i0000000000000000000000000000000000000000000000000000
χ694-44-44-4-44-24i−4i0000−4i4i22-2-22-2200−2i2i002i−2i000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000000000
χ704-44-44-4-44-24i−4i0000−4i4i22-2-22-2200−2i2i002i−2i000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000000000
χ714-44-44-4-44-2−4i4i00004i−4i22-2-22-22002i−2i00−2i2i000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000000000
χ724-44-44-4-44-2−4i4i00004i−4i22-2-22-22002i−2i00−2i2i000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000000000
χ734-44-4-444-44004i−4i−4i4i00-444-4-4-440000−4i4i004i−4i00000000000000000000000000000000000000000000000000
χ744-44-4-444-4400−4i4i4i−4i00-444-4-4-4400004i−4i00−4i4i00000000000000000000000000000000000000000000000000
χ754-44-4-444-4-2004i−4i−4i4i002-2-2222-200002i−2i00−2i2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000000
χ764-44-4-444-4-2004i−4i−4i4i002-2-2222-200002i−2i00−2i2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000000
χ774-44-4-444-4-200−4i4i4i−4i002-2-2222-20000−2i2i002i−2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000000
χ784-44-4-444-4-200−4i4i4i−4i002-2-2222-20000−2i2i002i−2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000000
χ794-4-444-44-4-24444-4-4-4-42222-2-2-24-4-2-22222-2-200000000-220000000000000000000000000000000000000000
χ804-4-444-44-4-2-4-4-4-444442222-2-2-24-422-2-2-2-22200000000-220000000000000000000000000000000000000000
χ814-4-44-44-44400000000-44-444-4-40000000000000000000000000000000000000000004i−4i0000000000000000
χ824-4-44-44-44400000000-44-444-4-4000000000000000000000000000000000000000000−4i4i0000000000000000
χ838888-8-8-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000

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