Finite Group Databasebeta

← Group #10695601

Character table — Group #10695601

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order12222222344666121212122444666612121212444444446121212121212121212121212121212121288242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-2000000002-2000000000000000000000022-2-2000000
χ10222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-2000000002-20000000000000000000000-2-222000000
χ1122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ1322222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ1422222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000
χ15222222-2-22222222222-22-2-2-2-22222-2-2000022-2-2-2-2000000002222-2-2-2-20000000000000000
χ16222222-2-22222222222-22-2-2-2-22222-2-20000-2-222-2-200000000-2-2-2-222220000000000000000
χ17222222-2-22-2-2222-2-2-2-2-2-222-2-222-2-22200000000-22000000000000000000000000002-20000
χ18222222-2-22-2-2222-2-2-2-2-2-222-2-222-2-22200000000-2200000000000000000000000000-220000
χ19222222-2-2-122-1-1-1-1-1-1-1-22-2-211-1-1-1-111000022-2-211−i3−i3−i3−i3i3i3i3i3-1-1-1-1111100−i3−i3i3i30000000000
χ20222222-2-2-122-1-1-1-1-1-1-1-22-2-211-1-1-1-111000022-2-211i3i3i3i3−i3−i3−i3−i3-1-1-1-1111100i3i3−i3−i30000000000
χ21222222-2-2-122-1-1-1-1-1-1-1-22-2-211-1-1-1-1110000-2-22211−i3−i3−i3−i3i3i3i3i31111-1-1-1-100i3i3−i3−i30000000000
χ22222222-2-2-122-1-1-1-1-1-1-1-22-2-211-1-1-1-1110000-2-22211i3i3i3i3−i3−i3−i3−i31111-1-1-1-100−i3−i3i3i30000000000
χ232222-2-2222222222222-2-22-222-2-2-2-22200000000-2-200000000000000000000000000002-200
χ242222-2-2222222222222-2-22-222-2-2-2-22200000000-2-20000000000000000000000000000-2200
χ252222-2-2222-2-2222-2-2-2-2-22-2222-2-222-2-222-2-20000-2222-2-222-2-2000000000000000000000000
χ262222-2-2222-2-2222-2-2-2-2-22-2222-2-222-2-2-2-2220000-22-2-222-2-222000000000000000000000000
χ272222-2-222-1-2-2-1-1-11111-22-22-1-111-1-11122-2-200001-1-1-111-1-11133−3−333−3−3003−33−30000000000
χ282222-2-222-1-2-2-1-1-11111-22-22-1-111-1-11122-2-200001-1-1-111-1-111−3−333−3−33300−33−330000000000
χ292222-2-222-1-2-2-1-1-11111-22-22-1-111-1-111-2-22200001-111-1-111-1-133−3−333−3−300−33−330000000000
χ302222-2-222-1-2-2-1-1-11111-22-22-1-111-1-111-2-22200001-111-1-111-1-1−3−333−3−333003−33−30000000000
χ312222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-200000000220000000000000000000000000000002-2
χ322222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-20000000022000000000000000000000000000000-22
χ332222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-22222000000002-200000000000000002i−2i2i−2i−2i2i0000000000
χ342222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-22222000000002-20000000000000000−2i2i−2i2i2i−2i0000000000
χ352222-2-2-2-2-1-2-2-1-1-11111222-21111-1-1-1-100000000-11−i3−i3i3i3i3i3−i3−i333−3−3−3−3332i−2i−iii−i0000000000
χ362222-2-2-2-2-1-2-2-1-1-11111222-21111-1-1-1-100000000-11−i3−i3i3i3i3i3−i3−i3−3−33333−3−3−2i2ii−i−ii0000000000
χ372222-2-2-2-2-1-2-2-1-1-11111222-21111-1-1-1-100000000-11i3i3−i3−i3−i3−i3i3i333−3−3−3−333−2i2ii−i−ii0000000000
χ382222-2-2-2-2-1-2-2-1-1-11111222-21111-1-1-1-100000000-11i3i3−i3−i3−i3−i3i3i3−3−33333−3−32i−2i−iii−i0000000000
χ3944444444-2-4-4-2-2-222224-4-4-4-2-2-2-2222200000000-2200000000000000000000000000000000
χ40444444-4-4-2-4-4-2-2-22222-4-44422-2-222-2-2000000002-200000000000000000000000000000000
χ414444-4-444-244-2-2-2-2-2-2-2-4-44-4-2-22222-2-2000000002200000000000000000000000000000000
χ424444-4-4-4-4-244-2-2-2-2-2-2-24-4-442222222200000000-2-200000000000000000000000000000000
χ4344-4-4004-44004-4-4000000004-400000000002-22-200000000002-22-22-22-20000000000000000
χ4444-4-4004-44004-4-4000000004-40000000000-22-220000000000-22-22-22-220000000000000000
χ4544-4-4004-4-200-2222323−23−230000-22000023−2300002-22-20000000000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000
χ4644-4-4004-4-200-2222323−23−230000-22000023−230000-22-2200000000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000
χ4744-4-4004-4-200-222−23−2323230000-220000−232300002-22-20000000000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000
χ4844-4-4004-4-200-222−23−2323230000-220000−23230000-22-2200000000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000
χ4944-4-400-444004-4-400000000-4400000000002-2-2200000000002-22-2-22-220000000000000000
χ5044-4-400-444004-4-400000000-440000000000-222-20000000000-22-222-22-20000000000000000
χ5144-4-400-44-200-2222323−23−2300002-20000−232300002-2-220000000000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000
χ5244-4-400-44-200-2222323−23−2300002-20000−23230000-222-200000000001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000
χ5344-4-400-44-200-222−23−23232300002-2000023−2300002-2-220000000000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000
χ5444-4-400-44-200-222−23−23232300002-2000023−230000-222-200000000001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000
χ554-44-4000044i−4i-44-44i−4i4i−4i000000000000000000000000000000000000000000002-22i−2i000000
χ564-44-4000044i−4i-44-44i−4i4i−4i00000000000000000000000000000000000000000000-22−2i2i000000
χ574-44-400004−4i4i-44-4−4i4i−4i4i000000000000000000000000000000000000000000002-2−2i2i000000
χ584-44-400004−4i4i-44-4−4i4i−4i4i00000000000000000000000000000000000000000000-222i−2i000000
χ594-4-444-400400-4-4400000000004-400002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ604-4-444-400400-4-4400000000004-40000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ614-4-444-400-20022-2−2i32i32i3−2i3000000-22−2i32i3002i−2i2i−2i0000002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000
χ624-4-444-400-20022-2−2i32i32i3−2i3000000-22−2i32i300−2i2i−2i2i000000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000
χ634-4-444-400-20022-22i3−2i3−2i32i3000000-222i3−2i3002i−2i2i−2i0000002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000
χ644-4-444-400-20022-22i3−2i3−2i32i3000000-222i3−2i300−2i2i−2i2i000000−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000
χ654-4-44-4400400-4-440000000000-4400002i−2i−2i2i0000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ664-4-44-4400400-4-440000000000-440000−2i2i2i−2i000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ674-4-44-4400-20022-2−2i32i32i3−2i30000002-22i3−2i3002i−2i−2i2i0000002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ684-4-44-4400-20022-2−2i32i32i3−2i30000002-22i3−2i300−2i2i2i−2i000000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ694-4-44-4400-20022-22i3−2i3−2i32i30000002-2−2i32i3002i−2i−2i2i0000002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11000000000000000000000000
χ704-4-44-4400-20022-22i3−2i3−2i32i30000002-2−2i32i300−2i2i2i−2i000000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11000000000000000000000000
χ718-88-80000-48i−8i4-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ728-88-80000-4−8i8i4-444i−4i4i−4i000000000000000000000000000000000000000000000000000000

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