Finite Group Databasebeta

← Group #10698417

Character table — Group #10698417

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order1222223444466612121212224466661212121222444444666661212121212121212121212121288242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ9222222222-2-22222222-2-22-2-2-22222-2-2000022-2-2-20000-200002222-2-2-2-20000000000000000
χ10222222222-2-22222222-2-22-2-2-22222-2-20000-2-222-20000-20000-2-2-2-222220000000000000000
χ112222222-2-222222-2-2-2-2-2-2-22-2-222-2-22200000000-20000200000000000000000022-2-2000000
χ122222222-2-222222-2-2-2-2-2-2-22-2-222-2-22200000000-200002000000000000000000-2-222000000
χ132222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-20000000020000-200000000000000000000002-20000
χ142222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-20000000020000-20000000000000000000000-220000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-11111-11111-1-1-1-1-1-1-1-1-2-211110000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-111111111111122-1-1-1-10000000000
χ19222222-122-2-2-1-1-1-1-1-1-1-2-22-211-1-1-1-111000022-2-21−i3−i3i3i31−i3−i3i3i3-1-1-1-1111100−i3−i3i3i30000000000
χ20222222-122-2-2-1-1-1-1-1-1-1-2-22-211-1-1-1-111000022-2-21i3i3−i3−i31i3i3−i3−i3-1-1-1-1111100i3i3−i3−i30000000000
χ21222222-122-2-2-1-1-1-1-1-1-1-2-22-211-1-1-1-1110000-2-2221−i3−i3i3i31−i3−i3i3i31111-1-1-1-100i3i3−i3−i30000000000
χ22222222-122-2-2-1-1-1-1-1-1-1-2-22-211-1-1-1-1110000-2-2221i3i3−i3−i31i3i3−i3−i31111-1-1-1-100−i3−i3i3i30000000000
χ232222-2-22222222222222-2-2-222-2-2-2-22200000000-20000-20000000000000000000000002i−2i00
χ242222-2-22222222222222-2-2-222-2-2-2-22200000000-20000-2000000000000000000000000−2i2i00
χ252222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-200000000200002000000000000000000000000002i−2i
χ262222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-20000000020000200000000000000000000000000−2i2i
χ272222-2-22-2-222222-2-2-2-2-222-2-2-2-2-222220000000020000-20000000000002i−2i2i−2i2i−2i0000000000
χ282222-2-22-2-222222-2-2-2-2-222-2-2-2-2-222220000000020000-2000000000000−2i2i−2i2i−2i2i0000000000
χ292222-2-22-2-2-2-2222-2-2-2-22-22222-2-222-2-222-2-20000-222222-2-2-2-2000000000000000000000000
χ302222-2-22-2-2-2-2222-2-2-2-22-22222-2-222-2-2-2-2220000-2-2-2-2-222222000000000000000000000000
χ312222-2-2-1-2-222-1-1-11111-222-21111-1-1-1-100000000-1−i3−i3i3i31i3i3−i3−i333−3−333−3−32i−2i−ii−ii0000000000
χ322222-2-2-1-2-222-1-1-11111-222-21111-1-1-1-100000000-1−i3−i3i3i31i3i3−i3−i3−3−333−3−333−2i2ii−ii−i0000000000
χ332222-2-2-1-2-222-1-1-11111-222-21111-1-1-1-100000000-1i3i3−i3−i31−i3−i3i3i333−3−333−3−3−2i2ii−ii−i0000000000
χ342222-2-2-1-2-222-1-1-11111-222-21111-1-1-1-100000000-1i3i3−i3−i31−i3−i3i3i3−3−333−3−3332i−2i−ii−ii0000000000
χ352222-2-2-1-2-2-2-2-1-1-111112-222-1-111-1-11122-2-200001-1-1-1-1-1111133−3−3−3−333003−3−330000000000
χ362222-2-2-1-2-2-2-2-1-1-111112-222-1-111-1-11122-2-200001-1-1-1-1-11111−3−33333−3−300−333−30000000000
χ372222-2-2-1-2-2-2-2-1-1-111112-222-1-111-1-111-2-222000011111-1-1-1-1-133−3−3−3−33300−333−30000000000
χ382222-2-2-1-2-2-2-2-1-1-111112-222-1-111-1-111-2-222000011111-1-1-1-1-1−3−33333−3−3003−3−330000000000
χ39444444-2-4-444-2-2-22222-4-4-4422-2-222-2-20000000020000-20000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2222244-4-4-2-2-2-2222200000000-2000020000000000000000000000000000
χ414444-4-4-24444-2-2-2-2-2-2-24-4-4-4-2-22222-2-2000000002000020000000000000000000000000000
χ424444-4-4-244-4-4-2-2-2-2-2-2-2-44-442222222200000000-20000-20000000000000000000000000000
χ4344-4-4004004i−4i4-4-4000000000000004i−4i00002-22i−2i00000000002-22-22i−2i2i−2i0000000000000000
χ4444-4-4004004i−4i4-4-4000000000000004i−4i0000-22−2i2i0000000000-22-22−2i2i−2i2i0000000000000000
χ4544-4-400400−4i4i4-4-400000000000000−4i4i00002-2−2i2i00000000002-22-2−2i2i−2i2i0000000000000000
χ4644-4-400400−4i4i4-4-400000000000000−4i4i0000-222i−2i0000000000-22-222i−2i2i−2i0000000000000000
χ4744-4-400-2004i−4i-2222323−23−230000−2i32i30000−2i2i00002-22i−2i0000000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000
χ4844-4-400-2004i−4i-2222323−23−230000−2i32i30000−2i2i0000-22−2i2i00000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000
χ4944-4-400-2004i−4i-222−23−23232300002i3−2i30000−2i2i00002-22i−2i0000000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000
χ5044-4-400-2004i−4i-222−23−23232300002i3−2i30000−2i2i0000-22−2i2i00000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000
χ5144-4-400-200−4i4i-2222323−23−2300002i3−2i300002i−2i00002-2−2i2i0000000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000
χ5244-4-400-200−4i4i-2222323−23−2300002i3−2i300002i−2i0000-222i−2i00000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000
χ5344-4-400-200−4i4i-222−23−2323230000−2i32i300002i−2i00002-2−2i2i0000000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000
χ5444-4-400-200−4i4i-222−23−2323230000−2i32i300002i−2i0000-222i−2i00000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000
χ554-44-40044i−4i00-44-44i−4i4i−4i000000000000000000000000000000000000000000002-22i−2i000000
χ564-44-40044i−4i00-44-44i−4i4i−4i00000000000000000000000000000000000000000000-22−2i2i000000
χ574-44-4004−4i4i00-44-4−4i4i−4i4i000000000000000000000000000000000000000000002-2−2i2i000000
χ584-44-4004−4i4i00-44-4−4i4i−4i4i00000000000000000000000000000000000000000000-222i−2i000000
χ594-4-444-440000-4-4400000000004-400002-22-2000002-22-202-22-2000000000000000000000000
χ604-4-444-440000-4-4400000000004-40000-22-2200000-22-220-22-22000000000000000000000000
χ614-4-444-4-2000022-2−2i32i32i3−2i3000000-22−2i32i3002-22-200000−1−i31+i3−1+i31−i30−1−i31+i3−1+i31−i3000000000000000000000000
χ624-4-444-4-2000022-2−2i32i32i3−2i3000000-22−2i32i300-22-22000001+i3−1−i31−i3−1+i301+i3−1−i31−i3−1+i3000000000000000000000000
χ634-4-444-4-2000022-22i3−2i3−2i32i3000000-222i3−2i3002-22-200000−1+i31−i3−1−i31+i30−1+i31−i3−1−i31+i3000000000000000000000000
χ644-4-444-4-2000022-22i3−2i3−2i32i3000000-222i3−2i300-22-22000001−i3−1+i31+i3−1−i301−i3−1+i31+i3−1−i3000000000000000000000000
χ654-4-44-4440000-4-440000000000-4400002-2-22000002-22-20-22-22000000000000000000000000
χ664-4-44-4440000-4-440000000000-440000-222-200000-22-2202-22-2000000000000000000000000
χ674-4-44-44-2000022-2−2i32i32i3−2i30000002-22i3−2i3002-2-2200000−1+i31−i3−1−i31+i301−i3−1+i31+i3−1−i3000000000000000000000000
χ684-4-44-44-2000022-2−2i32i32i3−2i30000002-22i3−2i300-222-2000001−i3−1+i31+i3−1−i30−1+i31−i3−1−i31+i3000000000000000000000000
χ694-4-44-44-2000022-22i3−2i3−2i32i30000002-2−2i32i3002-2-2200000−1−i31+i3−1+i31−i301+i3−1−i31−i3−1+i3000000000000000000000000
χ704-4-44-44-2000022-22i3−2i3−2i32i30000002-2−2i32i300-222-2000001+i3−1−i31−i3−1+i30−1−i31+i3−1+i31−i3000000000000000000000000
χ718-88-800-48i−8i004-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ728-88-800-4−8i8i004-444i−4i4i−4i000000000000000000000000000000000000000000000000000000

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