Finite Group Databasebeta

← Group #10695590

Character table — Group #10695590

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222222344666244466661212121212124444612121212121212121244881212121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-22222-2-2-22222-2-2-2-2-2-2000020000-2000000000000000022-2-200000000
χ10222222222-2-22222-2-2-22222-2-2-2-2-2-2000020000-20000000000000000-2-22200000000
χ1122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-1111122-2-2-1-1-1-11111000000000000
χ1422222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-11111-2-2221111-1-1-1-1000000000000
χ15222222-2-2222222-22-2-222-2-22222-2-20000-20000-20000000000000000000000002-200
χ16222222-2-2222222-22-2-222-2-22222-2-20000-20000-2000000000000000000000000-2200
χ17222222-2-22-2-2222-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-222222000000000000000000000000
χ18222222-2-22-2-2222-2-22222-2-2-2-2-2-222-2-222-222222-2-2-2-2000000000000000000000000
χ19222222-2-2-1-2-2-1-1-1-2-222-1-1111111-1-122-2-211111-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i3000000000000
χ20222222-2-2-1-2-2-1-1-1-2-222-1-1111111-1-122-2-211111-1-1-1-1-10000i3i3−i3−i3i3i3−i3−i3000000000000
χ21222222-2-2-1-2-2-1-1-1-2-222-1-1111111-1-1-2-2221-1-1-1-1-111110000−i3−i3i3i3i3i3−i3−i3000000000000
χ22222222-2-2-1-2-2-1-1-1-2-222-1-1111111-1-1-2-2221-1-1-1-1-111110000i3i3−i3−i3−i3−i3i3i3000000000000
χ232222-2-222222222-2-22-2-2-22222-2-2-2-20000-2000020000000000000000000022-2-20000
χ242222-2-222222222-2-22-2-2-22222-2-2-2-20000-20000200000000000000000000-2-2220000
χ252222-2-2222-2-2222-22-22-2-222-2-222220000-20000-200002-2002-22-20000000000000000
χ262222-2-2222-2-2222-22-22-2-222-2-222220000-20000-20000-2200-22-220000000000000000
χ272222-2-222-1-2-2-1-1-1-22-2211-1-111-1-1-1-100001−i3−i3i3i31−i3−i3i3i32-200-11-11−i3i3−i3i3000000000000
χ282222-2-222-1-2-2-1-1-1-22-2211-1-111-1-1-1-100001−i3−i3i3i31−i3−i3i3i3-22001-11-1i3−i3i3−i3000000000000
χ292222-2-222-1-2-2-1-1-1-22-2211-1-111-1-1-1-100001i3i3−i3−i31i3i3−i3−i32-200-11-11i3−i3i3−i3000000000000
χ302222-2-222-1-2-2-1-1-1-22-2211-1-111-1-1-1-100001i3i3−i3−i31i3i3−i3−i3-22001-11-1−i3i3−i3i3000000000000
χ312222-2-2-2-22222222-2-22-2-2-2-222-2-222000020000-20000002-200002-2-22000000000000
χ322222-2-2-2-22222222-2-22-2-2-2-222-2-222000020000-2000000-220000-222-2000000000000
χ332222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-20000200002000000000000000000000000002i−2i
χ342222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-2000020000200000000000000000000000000−2i2i
χ352222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-1−i3−i3i3i31i3i3−i3−i3002-2i3−i3−i3i3-111-1000000000000
χ362222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-1−i3−i3i3i31i3i3−i3−i300-22−i3i3i3−i31-1-11000000000000
χ372222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-1i3i3−i3−i31−i3−i3i3i3002-2−i3i3i3−i3-111-1000000000000
χ382222-2-2-2-2-122-1-1-12-2-221111-1-111-1-10000-1i3i3−i3−i31−i3−i3i3i300-22i3−i3−i3i31-1-11000000000000
χ3944444444-2-4-4-2-2-24-4-4-4-2-2-2-22222220000-2000020000000000000000000000000000
χ40444444-4-4-244-2-2-2-44-4-4-2-222-2-2-2-22200002000020000000000000000000000000000
χ414444-4-444-244-2-2-2-4-44-422-2-2-2-22222000020000-20000000000000000000000000000
χ424444-4-4-4-4-2-4-4-2-2-2444-4222222-2-2220000-20000-20000000000000000000000000000
χ4344-4-4000044i−4i-44-4000000004i−4i0000000000000000000000000000002-22i−2i00000000
χ4444-4-4000044i−4i-44-4000000004i−4i000000000000000000000000000000-22−2i2i00000000
χ4544-4-400004−4i4i-44-400000000−4i4i0000000000000000000000000000002-2−2i2i00000000
χ4644-4-400004−4i4i-44-400000000−4i4i000000000000000000000000000000-222i−2i00000000
χ474-44-4004-4400-4-440000004-40000002i−2i2i−2i02i−2i2i−2i02i−2i2i−2i000000000000000000000000
χ484-44-4004-4400-4-440000004-4000000−2i2i−2i2i0−2i2i−2i2i0−2i2i−2i2i000000000000000000000000
χ494-44-4004-4-20022-2000000-2200−2i32i3−2i32i32i−2i2i−2i02ζ7−2ζ72ζ11−2ζ1102ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ504-44-4004-4-20022-2000000-2200−2i32i3−2i32i3−2i2i−2i2i0−2ζ72ζ7−2ζ112ζ110−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ514-44-4004-4-20022-2000000-22002i3−2i32i3−2i32i−2i2i−2i02ζ11−2ζ112ζ7−2ζ702ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ524-44-4004-4-20022-2000000-22002i3−2i32i3−2i3−2i2i−2i2i0−2ζ112ζ11−2ζ72ζ70−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ534-44-400-44400-4-44000000-440000002i−2i−2i2i0−2i2i−2i2i02i−2i2i−2i000000000000000000000000
χ544-44-400-44400-4-44000000-44000000−2i2i2i−2i02i−2i2i−2i0−2i2i−2i2i000000000000000000000000
χ554-44-400-44-20022-20000002-200−2i32i32i3−2i32i−2i−2i2i0−2ζ112ζ11−2ζ72ζ702ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ564-44-400-44-20022-20000002-200−2i32i32i3−2i3−2i2i2i−2i02ζ11−2ζ112ζ7−2ζ70−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ574-44-400-44-20022-20000002-2002i3−2i3−2i32i32i−2i−2i2i0−2ζ72ζ7−2ζ112ζ1102ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ584-44-400-44-20022-20000002-2002i3−2i3−2i32i3−2i2i2i−2i02ζ7−2ζ72ζ11−2ζ110−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ594-4-444-4004004-4-400004-4000000000000000000000000000000000000002i−2i2i−2i0000
χ604-4-444-4004004-4-400004-400000000000000000000000000000000000000−2i2i−2i2i0000
χ614-4-44-44004004-4-40000-44000000000000000000000000000000000000002i−2i−2i2i0000
χ624-4-44-44004004-4-40000-4400000000000000000000000000000000000000−2i2i2i−2i0000
χ6388-8-80000-48i−8i4-4400000000−4i4i000000000000000000000000000000000000000000
χ6488-8-80000-4−8i8i4-44000000004i−4i000000000000000000000000000000000000000000
χ658-8-888-800-400-4440000-440000000000000000000000000000000000000000000000
χ668-8-88-8800-400-44400004-40000000000000000000000000000000000000000000000

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