Finite Group Databasebeta

← Group #10695545

Character table — Group #10695545

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order12222234466612121212224446666121212124444444461212121212121212121212121212121212882424242444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-1-1-111
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1111-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ92222222222222222-2-22-2-222-2-222-2-200000000-2-2000000000000000000000020-200000
χ102222222222222222-2-22-2-222-2-222-2-200000000-2-20000000000000000000000-20200000
χ112222222-2-2222-2-2-2-222-2-2-22222-2-2-2-2000000002-2000000000000000000000000002-200
χ122222222-2-2222-2-2-2-222-2-2-22222-2-2-2-2000000002-200000000000000000000000000-2200
χ132222222-2-2222-2-2-2-2-2-2-22222-2-2-2-22222-2-20000-222222-2-2-2-20000000000000000000000
χ142222222-2-2222-2-2-2-2-2-2-22222-2-2-2-222-2-2220000-22-2-2-2-222220000000000000000000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000
χ19222222-1-2-2-1-1-11111-2-2-222-1-11111-1-122-2-200001-1-1-1-1-111113333−3−3−3−30033−3−300000000
χ20222222-1-2-2-1-1-11111-2-2-222-1-11111-1-122-2-200001-1-1-1-1-11111−3−3−3−3333300−3−33300000000
χ21222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-2-22200001-11111-1-1-1-13333−3−3−3−300−3−33300000000
χ22222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-2-22200001-11111-1-1-1-1−3−3−3−333330033−3−300000000
χ232222-2-222222222222-2-2-22-2-2-2-2-2-2-2-200000000220000000000000000000000020-20000
χ242222-2-222222222222-2-2-22-2-2-2-2-2-2-2-2000000002200000000000000000000000-2020000
χ252222-2-22222222222-22-22-2-2-222-2-22200000000-2-200000000000000002-22-22-200000000
χ262222-2-22222222222-22-22-2-2-222-2-22200000000-2-20000000000000000-22-22-2200000000
χ272222-2-22-2-2222-2-2-2-22-222-2-2-2-2-2222200002i2i−2i−2i2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ282222-2-22-2-2222-2-2-2-22-222-2-2-2-2-222220000−2i−2i2i2i2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ292222-2-22-2-2222-2-2-2-2-222-22-2-22222-2-200000000-2200000000000000000000000000002-2
χ302222-2-22-2-2222-2-2-2-2-222-22-2-22222-2-200000000-220000000000000000000000000000-22
χ312222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000000011−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i32-2-11-1100000000
χ322222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-221-11-100000000
χ332222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000000011i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-221-11-100000000
χ342222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000000011i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i32-2-11-1100000000
χ352222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-100002i2i−2i−2i-11−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii003−3−3300000000
χ362222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-100002i2i−2i−2i-11i3i3−i3−i3−i3−i3i3i3−i−iii−i−iii00−333−300000000
χ372222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-10000−2i−2i2i2i-11−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i00−333−300000000
χ382222-2-2-1-2-2-1-1-111112-222-21111-1-1-1-10000−2i−2i2i2i-11i3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i003−3−3300000000
χ39444444-244-2-2-2-2-2-2-2-4-44-4-4-2-222-2-2220000000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2222244-4-4-4-2-2-2-2222200000000-22000000000000000000000000000000
χ414444-4-4-244-2-2-2-2-2-2-24-4-4-442222222200000000-2-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-22222-444-4422-2-2-2-222000000002-2000000000000000000000000000000
χ4344-4-44-44004-4-40000000004-400000000002-22-200000000002-22-22-22-200000000000000
χ4444-4-44-44004-4-40000000004-40000000000-22-220000000000-22-22-22-2200000000000000
χ4544-4-44-4-200-2222323−23−2300000-220023−230000002-22-20000000000−1+31−3−1+31−3−1−31+3−1−31+300000000000000
χ4644-4-44-4-200-2222323−23−2300000-220023−23000000-22-2200000000001−3−1+31−3−1+31+3−1−31+3−1−300000000000000
χ4744-4-44-4-200-222−23−23232300000-2200−23230000002-22-20000000000−1−31+3−1−31+3−1+31−3−1+31−300000000000000
χ4844-4-44-4-200-222−23−23232300000-2200−2323000000-22-2200000000001+3−1−31+3−1−31−3−1+31−3−1+300000000000000
χ4944-4-4-444004-4-4000000000-4400000000002i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5044-4-4-444004-4-4000000000-440000000000−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5144-4-4-44-200-2222323−23−23000002-200−23230000002i−2i−2i2i0000000000−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+ζ1100000000000000
χ5244-4-4-44-200-2222323−23−23000002-200−2323000000−2i2i2i−2i0000000000ζ2−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−ζ1100000000000000
χ5344-4-4-44-200-222−23−232323000002-20023−230000002i−2i−2i2i0000000000ζ2+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+ζ1100000000000000
χ5444-4-4-44-200-222−23−232323000002-20023−23000000−2i2i2i−2i0000000000−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−ζ1100000000000000
χ554-4-440044-4-44-44-44-400000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ564-4-440044-4-44-44-44-40000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ574-4-44004-44-44-4-44-4400000000000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ584-4-44004-44-44-4-44-440000000000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ594-4-4400-24-42-22-22-220000000−2i32i300−2i32i32i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ604-4-4400-24-42-22-22-220000000−2i32i300−2i32i3−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ614-4-4400-24-42-22-22-2200000002i3−2i3002i3−2i32i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ624-4-4400-24-42-22-22-2200000002i3−2i3002i3−2i3−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ634-4-4400-2-442-222-22-20000000−2i32i3002i3−2i32i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ644-4-4400-2-442-222-22-20000000−2i32i3002i3−2i3−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ654-4-4400-2-442-222-22-200000002i3−2i300−2i32i32i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ664-4-4400-2-442-222-22-200000002i3−2i300−2i32i3−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ678-88-800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-88-800-40044-443−43−434300000000000000000000000000000000000000000000000000000
χ698-88-800-40044-4−434343−4300000000000000000000000000000000000000000000000000000

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