Finite Group Databasebeta

← Group #10690816

Character table — Group #10690816

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
χ2922-22-2-22-222i−2i00002i−2i2-22-2-22-2002i−2i002i−2i001+i−1−i1−i−1+i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000002i−2i002-20000001−i−1+i1+i−1−i000000
χ3022-22-2-22-222i−2i00002i−2i2-22-2-22-2002i−2i002i−2i001+i−1−i1−i−1+i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−2i2i00-22000000−1+i1−i−1−i1+i000000
χ3122-22-2-22-222i−2i00002i−2i2-22-2-22-2002i−2i002i−2i00−1−i1+i−1+i1−i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000002i−2i002-2000000−1+i1−i−1−i1+i000000
χ3222-22-2-22-222i−2i00002i−2i2-22-2-22-2002i−2i002i−2i00−1−i1+i−1+i1−i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−2i2i00-220000001−i−1+i1+i−1−i000000
χ3322-22-2-22-22−2i2i0000−2i2i2-22-2-22-200−2i2i00−2i2i001−i−1+i1+i−1−i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000002i−2i00-22000000−1−i1+i−1+i1−i000000
χ3422-22-2-22-22−2i2i0000−2i2i2-22-2-22-200−2i2i00−2i2i001−i−1+i1+i−1−i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−2i2i002-20000001+i−1−i1−i−1+i000000
χ3522-22-2-22-22−2i2i0000−2i2i2-22-2-22-200−2i2i00−2i2i00−1+i1−i−1−i1+i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000002i−2i00-220000001+i−1−i1−i−1+i000000
χ3622-22-2-22-22−2i2i0000−2i2i2-22-2-22-200−2i2i00−2i2i00−1+i1−i−1−i1+i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−2i2i002-2000000−1−i1+i−1+i1−i000000
χ372-2-2-2-222222222-2-2-2-2-2-2222-2-22-222-2-2-2-22200002i−2i2i−2i2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382-2-2-2-222222222-2-2-2-2-2-2222-2-22-222-2-2-2-2220000−2i2i−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392-2-2-2-2222222-2-222-2-2-2-2222-2-2-222222-2-2-2-200000000-2200000000000000000000000000000000002i−2i2i−2i00
χ402-2-2-2-2222222-2-222-2-2-2-2222-2-2-222222-2-2-2-200000000-220000000000000000000000000000000000−2i2i−2i2i00
χ412-2-2-2-22222-2-222-2-222-2-2222-2-2-22-2-2-2-2222200000000-2200000000000000000000000000000000002-2-2200
χ422-2-2-2-22222-2-222-2-222-2-2222-2-2-22-2-2-2-2222200000000-220000000000000000000000000000000000-222-200
χ432-2-2-2-22222-2-2-2-22222-2-2222-2-22-2-2-22222-2-200002-2-222-20000000022-2-2-2-222000000000000000000000000
χ442-2-2-2-22222-2-2-2-22222-2-2222-2-22-2-2-22222-2-20000-222-22-200000000-2-22222-2-2000000000000000000000000
χ452-2-2-2-2222-12222-2-2-2-211-1-1-1112-2-1-11111-1-100002i−2i2i−2i-11−i3i3−i3i3−i3i3−i3i3−i−iii−i−iii00000000003−33−30000000000
χ462-2-2-2-2222-12222-2-2-2-211-1-1-1112-2-1-11111-1-100002i−2i2i−2i-11i3−i3i3−i3i3−i3i3−i3−i−iii−i−iii0000000000−33−330000000000
χ472-2-2-2-2222-12222-2-2-2-211-1-1-1112-2-1-11111-1-10000−2i2i−2i2i-11−i3i3−i3i3−i3i3−i3i3ii−i−iii−i−i0000000000−33−330000000000
χ482-2-2-2-2222-12222-2-2-2-211-1-1-1112-2-1-11111-1-10000−2i2i−2i2i-11i3−i3i3−i3i3−i3i3−i3ii−i−iii−i−i00000000003−33−30000000000
χ492-2-2-2-2222-1-2-2-2-2222211-1-1-1112-211-1-1-1-11100002-2-22-113−33−3−33−33-1-11111-1-10000000000−333−30000000000
χ502-2-2-2-2222-1-2-2-2-2222211-1-1-1112-211-1-1-1-11100002-2-22-11−33−333−33−3-1-11111-1-100000000003−3−330000000000
χ512-2-2-2-2222-1-2-2-2-2222211-1-1-1112-211-1-1-1-1110000-222-2-113−33−3−33−3311-1-1-1-11100000000003−3−330000000000
χ522-2-2-2-2222-1-2-2-2-2222211-1-1-1112-211-1-1-1-1110000-222-2-11−33−333−33−311-1-1-1-1110000000000−333−30000000000
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
χ55444-4-44-4-440000000044-44-4-4-40000000000000000000000000000000000004-40000000000000000000000
χ56444-4-44-4-440000000044-44-4-4-4000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-44-4-24i−4i00004i−4i-22-222-2200−2i2i00−2i2i002+2i−2−2i2−2i−2+2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000000000
χ5844-44-4-44-4-24i−4i00004i−4i-22-222-2200−2i2i00−2i2i00−2−2i2+2i−2+2i2−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000000000
χ5944-44-4-44-4-2−4i4i0000−4i4i-22-222-22002i−2i002i−2i002−2i−2+2i2+2i−2−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000000000
χ6044-44-4-44-4-2−4i4i0000−4i4i-22-222-22002i−2i002i−2i00−2+2i2−2i−2−2i2+2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000000000000000
χ6144-4-44-4-444004i−4i4i−4i004-4-4-44-4400004i−4i004i−4i00000000000000000000000000000000000000000000000000
χ6244-4-44-4-44400−4i4i−4i4i004-4-4-44-440000−4i4i00−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-44-4-44-2004i−4i4i−4i00-2222-22-20000−2i2i00−2i2i000000000000000000−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
χ6444-4-44-4-44-2004i−4i4i−4i00-2222-22-20000−2i2i00−2i2i000000000000000000ζ2−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
χ6544-4-44-4-44-200−4i4i−4i4i00-2222-22-200002i−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
χ6644-4-44-4-44-200−4i4i−4i4i00-2222-22-200002i−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
χ674-444-4-4-444004i−4i−4i4i00-44-4-444-40000−4i4i004i−4i00000000000000000000000000000000000000000000000000
χ684-444-4-4-44400−4i4i4i−4i00-44-4-444-400004i−4i00−4i4i00000000000000000000000000000000000000000000000000
χ694-444-4-4-44-2004i−4i−4i4i002-222-2-2200002i−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
χ704-444-4-4-44-2004i−4i−4i4i002-222-2-2200002i−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
χ714-444-4-4-44-200−4i4i4i−4i002-222-2-220000−2i2i002i−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
χ724-444-4-4-44-200−4i4i4i−4i002-222-2-220000−2i2i002i−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
χ734-44-44-44-444i−4i0000−4i4i-444-4-4-44004i−4i00−4i4i0000000000000000000000000000000000000000000000000000
χ744-44-44-44-44−4i4i00004i−4i-444-4-4-4400−4i4i004i−4i0000000000000000000000000000000000000000000000000000
χ754-44-44-44-4-24i−4i0000−4i4i2-2-2222-200−2i2i002i−2i000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000000000
χ764-44-44-44-4-24i−4i0000−4i4i2-2-2222-200−2i2i002i−2i000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000000000
χ774-44-44-44-4-2−4i4i00004i−4i2-2-2222-2002i−2i00−2i2i000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000000000
χ784-44-44-44-4-2−4i4i00004i−4i2-2-2222-2002i−2i00−2i2i000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000000000
χ794-4-4444-4-4400000000-4-4-44-44400000000000000000000000000000000000000004i−4i000000000000000000
χ804-4-4444-4-4400000000-4-4-44-4440000000000000000000000000000000000000000−4i4i000000000000000000
χ814-4-4-4-4444-244-4-444-4-422-2-2-222-44-2-2-2-22222000000002-20000000000000000000000000000000000000000
χ824-4-4-4-4444-2-4-444-4-44422-2-2-222-442222-2-2-2-2000000002-20000000000000000000000000000000000000000
χ83888-8-88-8-8-400000000-4-44-4444000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-400000000444-44-4-4000000000000000000000000000000000000000000000000000000000000

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