Finite Group Databasebeta

← Group #10695984

Character table — Group #10695984

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122222344446664444661212121212121212444412121212121212121212246688121224242424444488882488
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
χ51111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2222-22-2-222-2-2-2-222-2-20000-200002000000000000000022-2-200000000
χ10222222222-2-2222-22-2-222-2-2-2-222-2-20000-2000020000000000000000-2-22200000000
χ112222222-2-222222-2-22-2222222-2-2-2-20000-20000-20000000000000000000000002-200
χ122222222-2-222222-2-22-2222222-2-2-2-20000-20000-2000000000000000000000000-2200
χ132222222-2-2-2-22222-2-2222-2-2-2-2-2-22222-2-222222-2-2-2-2-2000000000000000000000000
χ142222222-2-2-2-22222-2-2222-2-2-2-2-2-222-2-2222-2-2-2-2-22222000000000000000000000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-1111122-1-1-2-2-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111-11111-2-2112211-1-1-1-1000000000000
χ19222222-1-2-2-2-2-1-1-12-2-22-1-1111111-1-122-2-2-1-1-1-1-11111100−i3i300−i3i3−i3−i3i3i3000000000000
χ20222222-1-2-2-2-2-1-1-12-2-22-1-1111111-1-122-2-2-1-1-1-1-11111100i3−i300i3−i3i3i3−i3−i3000000000000
χ21222222-1-2-2-2-2-1-1-12-2-22-1-1111111-1-1-2-222-111111-1-1-1-100−i3i300−i3i3i3i3−i3−i3000000000000
χ22222222-1-2-2-2-2-1-1-12-2-22-1-1111111-1-1-2-222-111111-1-1-1-100i3−i300i3−i3−i3−i3i3i3000000000000
χ232222-2-2222222222-2-2-2-2-222-2-222-2-2000020000-2000000000000000000000000002-2
χ242222-2-2222222222-2-2-2-2-222-2-222-2-2000020000-200000000000000000000000000-22
χ252222-2-2222-2-2222-2-222-2-2-2-22222220000-20000-2000000002-2002-22-2000000000000
χ262222-2-2222-2-2222-2-222-2-2-2-22222220000-20000-200000000-2200-22-22000000000000
χ272222-2-22-2-222222-22-22-2-222-2-2-2-2220000-20000200002-22200-2-20000000000000000
χ282222-2-22-2-222222-22-22-2-222-2-2-2-2220000-2000020000-22-2-200220000000000000000
χ292222-2-22-2-2-2-2222222-2-2-2-2-222-2-2-2-20000200002000000000000000000002i2i−2i−2i0000
χ302222-2-22-2-2-2-2222222-2-2-2-2-222-2-2-2-2000020000200000000000000000000−2i−2i2i2i0000
χ312222-2-2-122-2-2-1-1-1-2-2221111-1-1-1-1-1-100001−i3−i3i3i31−i3−i3i3i300−i3i32-2i3−i3-11-11000000000000
χ322222-2-2-122-2-2-1-1-1-2-2221111-1-1-1-1-1-100001−i3−i3i3i31−i3−i3i3i300i3−i3-22−i3i31-11-1000000000000
χ332222-2-2-122-2-2-1-1-1-2-2221111-1-1-1-1-1-100001i3i3−i3−i31i3i3−i3−i300−i3i3-22i3−i31-11-1000000000000
χ342222-2-2-122-2-2-1-1-1-2-2221111-1-1-1-1-1-100001i3i3−i3−i31i3i3−i3−i300i3−i32-2−i3i3-11-11000000000000
χ352222-2-2-1-2-222-1-1-1-22-2211-1-11111-1-100001−i3−i3i3i3-1i3i3−i3−i32-2-1-10011−i3i3i3−i3000000000000
χ362222-2-2-1-2-222-1-1-1-22-2211-1-11111-1-100001−i3−i3i3i3-1i3i3−i3−i3-221100-1-1i3−i3−i3i3000000000000
χ372222-2-2-1-2-222-1-1-1-22-2211-1-11111-1-100001i3i3−i3−i3-1−i3−i3i3i32-2-1-10011i3−i3−i3i3000000000000
χ382222-2-2-1-2-222-1-1-1-22-2211-1-11111-1-100001i3i3−i3−i3-1−i3−i3i3i3-221100-1-1−i3i3i3−i3000000000000
χ39444444-244-4-4-2-2-2-44-4-4-2-22222-2-222000020000-20000000000000000000000000000
χ40444444-2-4-444-2-2-2-4-44-4-2-2-2-2-2-2222200002000020000000000000000000000000000
χ414444-4-4-24444-2-2-24-4-4-422-2-222-2-2220000-2000020000000000000000000000000000
χ424444-4-4-2-4-4-4-4-2-2-2444-42222-2-222220000-20000-20000000000000000000000000000
χ4344-4-40044i−4i00-44-400000000004i−4i002-22i−2i02-22-202i−2i2i−2i000000000000000000000000
χ4444-4-40044i−4i00-44-400000000004i−4i00-22−2i2i0-22-220−2i2i−2i2i000000000000000000000000
χ4544-4-4004−4i4i00-44-40000000000−4i4i002-2−2i2i02-22-20−2i2i−2i2i000000000000000000000000
χ4644-4-4004−4i4i00-44-40000000000−4i4i00-222i−2i0-22-2202i−2i2i−2i000000000000000000000000
χ4744-4-400-24i−4i002-220000000023−23−2i2i−2i32i32-22i−2i0−1−i31+i3−1+i31−i302ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ4844-4-400-24i−4i002-220000000023−23−2i2i−2i32i3-22−2i2i01+i3−1−i31−i3−1+i30−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ4944-4-400-24i−4i002-2200000000−2323−2i2i2i3−2i32-22i−2i0−1+i31−i3−1−i31+i302ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ5044-4-400-24i−4i002-2200000000−2323−2i2i2i3−2i3-22−2i2i01−i3−1+i31+i3−1−i30−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ5144-4-400-2−4i4i002-220000000023−232i−2i2i3−2i32-2−2i2i0−1+i31−i3−1−i31+i30−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ5244-4-400-2−4i4i002-220000000023−232i−2i2i3−2i3-222i−2i01−i3−1+i31+i3−1−i302ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ5344-4-400-2−4i4i002-2200000000−23232i−2i−2i32i32-2−2i2i0−1−i31+i3−1+i31−i30−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ5444-4-400-2−4i4i002-2200000000−23232i−2i−2i32i3-222i−2i01+i3−1−i31−i3−1+i302ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ554-44-44-440000-4-4400004-4000000000000000000000000000000000000002i−2i2i−2i0000
χ564-44-44-440000-4-4400004-400000000000000000000000000000000000000−2i2i−2i2i0000
χ574-44-4-4440000-4-440000-44000000000000000000000000000000000000002-2-220000
χ584-44-4-4440000-4-440000-4400000000000000000000000000000000000000-222-20000
χ594-4-44004004-44-4-40000004-4000000000000000000000000000000002i−2i2i−2i00000000
χ604-4-44004004-44-4-40000004-400000000000000000000000000000000−2i2i−2i2i00000000
χ614-4-4400400-444-4-4000000-44000000000000000000000000000000002i−2i−2i2i00000000
χ624-4-4400400-444-4-4000000-4400000000000000000000000000000000−2i2i2i−2i00000000
χ638-88-88-8-4000044-40000-440000000000000000000000000000000000000000000000
χ648-88-8-88-4000044-400004-40000000000000000000000000000000000000000000000
χ658-8-8800-4008-8-444000000-4400000000000000000000000000000000000000000000
χ668-8-8800-400-88-4440000004-400000000000000000000000000000000000000000000

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