Finite Group Databasebeta

← Group #11772002

Character table — Group #11772002

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222222222444444444444444444448888888888888888888888824242424242424242424242448484848484872727272
order1223344666612123666688881212121212121224242424412121212121212122424242424242424242424242424161616164848484848484848441212121216161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-1-1-111ii−i−i
χ6111111111111111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1111-1-1−i−iii
χ7111111111111111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-1-1-111−i−iii
χ8111111111111111111-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1111-1-1ii−i−i
χ922222222222222222222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000
χ10222222222222222222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000
χ112222-1222-1-1-122-12-1-1-122222-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000022-1-1-1-10000
χ122222-1222-1-1-122-12-1-1-122222-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2-211110000
χ132222-1222-1-1-122-12-1-1-122-2-22-1-1-1-1-1-12222-211-2-21111-1-1-1-1-1-1-2-211111100000000000000−i3i3−i3i30000
χ142222-1222-1-1-122-12-1-1-122-2-22-1-1-1-1-1-12222-211-2-21111-1-1-1-1-1-1-2-211111100000000000000i3−i3i3−i30000
χ152222-1222-1-1-122-12-1-1-1-2-2222-1-1-1-1-1-1-2-2-2-2-211-2-2111111111122-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ162222-1222-1-1-122-12-1-1-1-2-2222-1-1-1-1-1-1-2-2-2-2-211-2-2111111111122-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ172222-1222-1-1-122-12-1-1-1-2-2-2-22-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-1111111-2-21111110000000000002-211-1-10000
χ182222-1222-1-1-122-12-1-1-1-2-2-2-22-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-1111111-2-2111111000000000000-22-1-1110000
χ19222-1222-1222-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ20222-1222-1222-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111110000000000
χ21222-1222-1222-1-1-1-1-1-1-122-2-2-122-1-1-1-1-1-1-1-1-2-2-211111122-1-1-1-111-2-211110000−i3−i3i3i3−i3−i3i3i30000000000
χ22222-1222-1222-1-1-1-1-1-1-122-2-2-122-1-1-1-1-1-1-1-1-2-2-211111122-1-1-1-111-2-211110000i3i3−i3−i3i3i3−i3−i30000000000
χ23222-1222-1222-1-1-1-1-1-1-1-2-222-122-1-1-1-11111-2-2-2111111-2-21111-1-122-1-1-1-1000033−3−3−3−3330000000000
χ24222-1222-1222-1-1-1-1-1-1-1-2-222-122-1-1-1-11111-2-2-2111111-2-21111-1-122-1-1-1-10000−3−33333−3−30000000000
χ25222-1222-1222-1-1-1-1-1-1-1-2-2-2-2-122-1-1-1-11111222-1-1-1-1-1-1-2-2111111-2-211112i2i−2i−2i−i−i−i−iiiii0000000000
χ26222-1222-1222-1-1-1-1-1-1-1-2-2-2-2-122-1-1-1-11111222-1-1-1-1-1-1-2-2111111-2-21111−2i−2i2i2iiiii−i−i−i−i0000000000
χ2722-2222-22-2-22222-22-2-2002i−2i-22-222-2-200000000000000000002i−2i2i−2i2i2i−2i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ2822-2222-22-2-22222-22-2-2002i−2i-22-222-2-200000000000000000002i−2i2i−2i2i2i−2i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ2922-2222-22-2-22222-22-2-200−2i2i-22-222-2-20000000000000000000−2i2i−2i2i−2i−2i2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ3022-2222-22-2-22222-22-2-200−2i2i-22-222-2-20000000000000000000−2i2i−2i2i−2i−2i2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ3122-222-222-2-22-2-22-22-2-22i−2i002-22-2-2222i2i−2i−2i0000000002i−2i2i2i−2i−2i000000000000000000000000001+i−1−i1−i−1+i
χ3222-222-222-2-22-2-22-22-2-22i−2i002-22-2-2222i2i−2i−2i0000000002i−2i2i2i−2i−2i00000000000000000000000000−1−i1+i−1+i1−i
χ3322-222-222-2-22-2-22-22-2-2−2i2i002-22-2-222−2i−2i2i2i000000000−2i2i−2i−2i2i2i000000000000000000000000001−i−1+i1+i−1−i
χ3422-222-222-2-22-2-22-22-2-2−2i2i002-22-2-222−2i−2i2i2i000000000−2i2i−2i−2i2i2i00000000000000000000000000−1+i1−i−1−i1+i
χ3522-2-122-2-1-2-22-1-1-11-111002i−2i12-2-1-111−i3i3−i3i30003−333−3−300−i3i3−i3i3−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ110000000000
χ3622-2-122-2-1-2-22-1-1-11-111002i−2i12-2-1-111−i3i3−i3i30003−333−3−300−i3i3−i3i3−ii2i−2i−i−iii−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ110000000000
χ3722-2-122-2-1-2-22-1-1-11-111002i−2i12-2-1-111i3−i3i3−i3000−33−3−33300i3−i3i3−i3−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70000000000
χ3822-2-122-2-1-2-22-1-1-11-111002i−2i12-2-1-111i3−i3i3−i3000−33−3−33300i3−i3i3−i3−ii2i−2i−i−iii−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70000000000
χ3922-2-122-2-1-2-22-1-1-11-11100−2i2i12-2-1-111−i3i3−i3i3000−33−3−33300−i3i3−i3i3i−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110000000000
χ4022-2-122-2-1-2-22-1-1-11-11100−2i2i12-2-1-111−i3i3−i3i3000−33−3−33300−i3i3−i3i3i−i−2i2iii−i−i−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110000000000
χ4122-2-122-2-1-2-22-1-1-11-11100−2i2i12-2-1-111i3−i3i3−i30003−333−3−300i3−i3i3−i3i−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ70000000000
χ4222-2-122-2-1-2-22-1-1-11-11100−2i2i12-2-1-111i3−i3i3−i30003−333−3−300i3−i3i3−i3i−i−2i2iii−i−i−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ70000000000
χ4344444-4-44444-4-4444440000-4-4-4-4-4-4-40000000000000000000000000000000000000000000000000
χ444444-2-4-44-2-2-2-4-4-24-2-2-20000-422222200000−2i32i300−2i32i3−2i32i3000000000000000000000000000000000000
χ454444-2-4-44-2-2-2-4-4-24-2-2-20000-4222222000002i3−2i3002i3−2i32i3−2i3000000000000000000000000000000000000
χ46444-24-4-4-244422-2-2-2-2-200002-4-4222223−23−23230000000000023−23−2323000000000000000000000000000000
χ47444-24-4-4-244422-2-2-2-2-200002-4-42222−232323−2300000000000−232323−23000000000000000000000000000000
χ48444-2-244-2-2-2-2-2-21-21114444-2-2-21111-2-2-2-24-2-2-2-21111-2-21111-2-2-2-211110000000000000000000000
χ49444-2-244-2-2-2-2-2-21-211144-4-4-2-2-21111-2-2-2-2-42222-1-1-1-1-2-211112222-1-1-1-10000000000000000000000
χ50444-2-244-2-2-2-2-2-21-2111-4-444-2-2-211112222-42222-1-1-1-122-1-1-1-1-2-2-2-211110000000000000000000000
χ51444-2-244-2-2-2-2-2-21-2111-4-4-4-4-2-2-2111122224-2-2-2-2111122-1-1-1-12222-1-1-1-10000000000000000000000
χ52444-2-2-4-4-2-2-2-2221-21110000222-1-1-1-123−23−23230−2i32i300i3−i3i3−i300−333−300003i−3i3i−3i0000000000000000000000
χ53444-2-2-4-4-2-2-2-2221-21110000222-1-1-1-123−23−232302i3−2i300−i3i3−i3i300−333−30000−3i3i−3i3i0000000000000000000000
χ54444-2-2-4-4-2-2-2-2221-21110000222-1-1-1-1−232323−230−2i32i300i3−i3i3−i3003−3−330000−3i3i−3i3i0000000000000000000000
χ55444-2-2-4-4-2-2-2-2221-21110000222-1-1-1-1−232323−2302i3−2i300−i3i3−i3i3003−3−3300003i−3i3i−3i0000000000000000000000
χ5644-44-24-4422-244-2-4-222004i−4i-4-22-2-22200000000000000000004i−4i−2i2i−2i−2i2i2i0000000000000000000000
χ5744-44-24-4422-244-2-4-22200−4i4i-4-22-2-2220000000000000000000−4i4i2i−2i2i2i−2i−2i0000000000000000000000
χ5844-44-2-44422-2-4-4-2-4-2224i−4i0042-222-2-24i4i−4i−4i000000000−2i2i−2i−2i2i2i000000000000000000000000000000
χ5944-44-2-44422-2-4-4-2-4-222−4i4i0042-222-2-2−4i−4i4i4i0000000002i−2i2i2i−2i−2i000000000000000000000000000000
χ6044-4-24-44-2-4-4422-22-2224i−4i00-2-4422-2-2−2i−2i2i2i0000000004i−4i−2i−2i2i2i000000000000000000000000000000
χ6144-4-24-44-2-4-4422-22-222−4i4i00-2-4422-2-22i2i−2i−2i000000000−4i4i2i2i−2i−2i000000000000000000000000000000
χ6244-4-2-24-4-222-2-2-2121-1-1004i−4i2-2211-1-1−2i32i3−2i32i300023−23−3−33300i3−i3i3−i3−2i2i−2i2iii−i−i0000000000000000000000
χ6344-4-2-24-4-222-2-2-2121-1-1004i−4i2-2211-1-12i3−2i32i3−2i3000−232333−3−300−i3i3−i3i3−2i2i−2i2iii−i−i0000000000000000000000
χ6444-4-2-24-4-222-2-2-2121-1-100−4i4i2-2211-1-1−2i32i3−2i32i3000−232333−3−300i3−i3i3−i32i−2i2i−2i−i−iii0000000000000000000000
χ6544-4-2-24-4-222-2-2-2121-1-100−4i4i2-2211-1-12i3−2i32i3−2i300023−23−3−33300−i3i3−i3i32i−2i2i−2i−i−iii0000000000000000000000
χ6644-4-2-2-44-222-222121-1-14i−4i00-22-2-1-111−2i−2i2i2i000003i−3i−3i3i−2i2iii−i−i00003-3-330000000000000000000000
χ6744-4-2-2-44-222-222121-1-14i−4i00-22-2-1-111−2i−2i2i2i00000−3i3i3i−3i−2i2iii−i−i0000-333-30000000000000000000000
χ6844-4-2-2-44-222-222121-1-1−4i4i00-22-2-1-1112i2i−2i−2i000003i−3i−3i3i2i−2i−i−iii0000-333-30000000000000000000000
χ6944-4-2-2-44-222-222121-1-1−4i4i00-22-2-1-1112i2i−2i−2i00000−3i3i3i−3i2i−2i−i−iii00003-3-330000000000000000000000
χ708-808800-800-80080-800000000000000000000000000000000000000000000000000000000000000
χ718-808-400-8−4i34i3400-404−4i34i3000000000000000000000000000000000000000000000000000000000000
χ728-808-400-84i3−4i3400-4044i3−4i3000000000000000000000000000000000000000000000000000000000000
χ738-80-4800400-843−43-40400000000043−43000000000000000000000000000000000000000000000000000
χ748-80-4800400-8−4343-404000000000−4343000000000000000000000000000000000000000000000000000
χ758-80-4-4004−4i34i3443−4320-22i3−2i30000000−23236i−6i0000000000000000000000000000000000000000000000000
χ768-80-4-4004−4i34i34−434320-22i3−2i3000000023−23−6i6i0000000000000000000000000000000000000000000000000
χ778-80-4-40044i3−4i3443−4320-2−2i32i30000000−2323−6i6i0000000000000000000000000000000000000000000000000
χ788-80-4-40044i3−4i34−434320-2−2i32i3000000023−236i−6i0000000000000000000000000000000000000000000000000

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