Finite Group Databasebeta

← Group #11771741

Character table — Group #11771741

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222222222444444444444444444448888888888888888888888824242424242424242424242448484848484872727272
order1223344666612122346666668812121212121212121266681212122424242424242424242424242424242444441212121212121212441212121216161616
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
χ51111111111111-11-11111-1-1-1-1-1-11111111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-1-1-111ii−i−i
χ61111111111111-11-11111-1-1-1-1-1-11111111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1111-1-1−i−iii
χ71111111111111-11-11111-1-1-1-1-1-11111111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-1-1-111−i−iii
χ81111111111111-11-11111-1-1-1-1-1-11111111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1111-1-1ii−i−i
χ92222222222222222222222-2-2222222222222-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ102222222222222-22-22222-2-222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000
χ1122222-2-22222-2-222-222222200-2-2-2-2-2-2-2-2-22220-2-2-200000000000000000000000000000000002−22−2
χ1222222-2-22222-2-222-222222200-2-2-2-2-2-2-2-2-22220-2-2-20000000000000000000000000000000000−22−22
χ1322222-2-22222-2-2-2222222-2-20022-2-2-2-2-2-2-2-2-2-202220000000000000000000000000000000000−i2i2i2−i2
χ1422222-2-22222-2-2-2222222-2-20022-2-2-2-2-2-2-2-2-2-202220000000000000000000000000000000000i2−i2−i2i2
χ152222-1222-1-1-1222-122-1-1-1222222-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000022-1-1-1-10000
χ162222-1222-1-1-1222-122-1-1-1222222-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2-211110000
χ172222-1222-1-1-1222-122-1-1-122-2-222-1-1-12-1-1-1-1-1-1-2-1-1-1-2-2111111-2-211111100000000000000−i3i3−i3i30000
χ182222-1222-1-1-1222-122-1-1-122-2-222-1-1-12-1-1-1-1-1-1-2-1-1-1-2-2111111-2-211111100000000000000i3−i3i3−i30000
χ192222-1222-1-1-122-2-1-22-1-1-1-2-222-2-2-1-1-12-1-1-1111-2111-2-211111122-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ202222-1222-1-1-122-2-1-22-1-1-1-2-222-2-2-1-1-12-1-1-1111-2111-2-211111122-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ212222-1222-1-1-122-2-1-22-1-1-1-2-2-2-2-2-2-1-1-12-1-1-1111211122-1-1-1-1-1-1-2-21111110000000000002-211-1-10000
χ222222-1222-1-1-122-2-1-22-1-1-1-2-2-2-2-2-2-1-1-12-1-1-1111211122-1-1-1-1-1-1-2-2111111000000000000-22-1-1110000
χ23222-1222-1222-1-12-12-1-1-1-1-1-122-1-12-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ24222-1222-1222-1-12-12-1-1-1-1-1-122-1-12-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111110000000000
χ25222-1222-1222-1-12-12-1-1-1-1-1-1-2-2-1-12-1-1-12-1-12-1-1-22-1-111-2-2111111-2-211110000−i3−i3i3i3−i3−i3i3i30000000000
χ26222-1222-1222-1-12-12-1-1-1-1-1-1-2-2-1-12-1-1-12-1-12-1-1-22-1-111-2-2111111-2-211110000i3i3−i3−i3i3i3−i3−i30000000000
χ27222-1222-1222-1-1-2-1-2-1-1-1-11122112-1-1-12-1-1-211-2-21111-2-21111-1-122-1-1-1-1000033−3−3−3−3330000000000
χ28222-1222-1222-1-1-2-1-2-1-1-1-11122112-1-1-12-1-1-211-2-21111-2-21111-1-122-1-1-1-10000−3−33333−3−30000000000
χ29222-1222-1222-1-1-2-1-2-1-1-1-111-2-2112-1-1-12-1-1-2112-211-1-122-1-1-1-111-2-211112i2i−2i−2i−i−i−i−iiiii0000000000
χ30222-1222-1222-1-1-2-1-2-1-1-1-111-2-2112-1-1-12-1-1-2112-211-1-122-1-1-1-111-2-21111−2i−2i2i2iiiii−i−i−i−i0000000000
χ3122-2222-22-2-2222020-2-2-22002i−2i00222-2-2-2-20000000000000002i−2i2i−2i2i2i−2i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ3222-2222-22-2-2222020-2-2-22002i−2i00222-2-2-2-20000000000000002i−2i2i−2i2i2i−2i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ3322-2222-22-2-2222020-2-2-2200−2i2i00222-2-2-2-2000000000000000−2i2i−2i2i−2i−2i2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ3422-2222-22-2-2222020-2-2-2200−2i2i00222-2-2-2-2000000000000000−2i2i−2i2i−2i−2i2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ3522-2-122-2-1-2-22-1-10-10111-1−i3i32i−2i−i3i32-1-11-2110−i3i300−i3i33−30033−3−3−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000000000
χ3622-2-122-2-1-2-22-1-10-10111-1−i3i32i−2i−i3i32-1-11-2110−i3i300−i3i33−30033−3−3−ii2i−2i−i−iii−1−i1+i−1+i1−iζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000000000
χ3722-2-122-2-1-2-22-1-10-10111-1−i3i3−2i2i−i3i32-1-11-2110−i3i300−i3i3−3300−3−333i−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000000000
χ3822-2-122-2-1-2-22-1-10-10111-1−i3i3−2i2i−i3i32-1-11-2110−i3i300−i3i3−3300−3−333i−i−2i2iii−i−i−1+i1−i−1−i1+iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000000000
χ3922-2-122-2-1-2-22-1-10-10111-1i3−i32i−2ii3−i32-1-11-2110i3−i300i3−i3−3300−3−333−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000000000
χ4022-2-122-2-1-2-22-1-10-10111-1i3−i32i−2ii3−i32-1-11-2110i3−i300i3−i3−3300−3−333−ii2i−2i−i−iii−1−i1+i−1+i1−iζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000000000
χ4122-2-122-2-1-2-22-1-10-10111-1i3−i3−2i2ii3−i32-1-11-2110i3−i300i3−i33−30033−3−3i−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000000000
χ4222-2-122-2-1-2-22-1-10-10111-1i3−i3−2i2ii3−i32-1-11-2110i3−i300i3−i33−30033−3−3i−i−2i2iii−i−i−1+i1−i−1−i1+iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000000000
χ434444-2-4-44-2-2-2-4-44-2-44-2-2-24400-4-4222-4222-2-2-2022200000000000000000000000000000000000000
χ444444-2-4-44-2-2-2-4-4-4-244-2-2-2-4-40044222-42222220-2-2-200000000000000000000000000000000000000
χ45444-24-4-4-2444224-2-4-2-2-2-2-2-20022-4222-4224-2-20-42200000000000000000000000000000000000000
χ46444-24-4-4-244422-4-24-2-2-2-22200-2-2-4222-422-42204-2-200000000000000000000000000000000000000
χ47444-2-244-2-2-2-2-2-2414-2111-2-244-2-2-211-2-211-2114-211-2-2-2-21111-2-2-2-211110000000000000000000000
χ48444-2-244-2-2-2-2-2-2414-2111-2-2-4-4-2-2-211-2-211-211-4-2112222-1-1-1-12222-1-1-1-10000000000000000000000
χ49444-2-244-2-2-2-2-2-2-41-4-2111224422-211-2-2112-1-1-42-1-12222-1-1-1-1-2-2-2-211110000000000000000000000
χ50444-2-244-2-2-2-2-2-2-41-4-211122-4-422-211-2-2112-1-142-1-1-2-2-2-211112222-1-1-1-10000000000000000000000
χ51444-2-2-4-4-2-2-2-22241-4-2111-2-200222-1-122-1-1-21102-1-100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000
χ52444-2-2-4-4-2-2-2-22241-4-2111-2-200222-1-122-1-1-21102-1-10000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000
χ53444-2-2-4-4-2-2-2-222-414-21112200-2-22-1-122-1-12-1-10-21100003i−3i3i−3i0000−3i3i−3i3i0000000000000000000000
χ54444-2-2-4-4-2-2-2-222-414-21112200-2-22-1-122-1-12-1-10-2110000−3i3i−3i3i00003i−3i3i−3i0000000000000000000000
χ5544-444-444-4-44-4-4040-4-4-44000000-4-4-44444000000000000000000000000000000000000000000000
χ5644-44-24-4422-2440-20-422-2004i−4i00-2-2-2-42220000000000000004i−4i−2i2i−2i−2i2i2i0000000000000000000000
χ5744-44-24-4422-2440-20-422-200−4i4i00-2-2-2-4222000000000000000−4i4i2i−2i2i2i−2i−2i0000000000000000000000
χ5844-44-2-44422-2-4-40-20-422-20000002224-2-2-2000000000−2i32i3−2i32i32i3−2i3000000000000000000000000000000
χ5944-44-2-44422-2-4-40-20-422-20000002224-2-2-20000000002i3−2i32i3−2i3−2i32i3000000000000000000000000000000
χ6044-4-24-44-2-4-44220-20222-2−2i32i3002i3−2i3-422-24-2-20−2i32i3002i3−2i300000000000000000000000000000000000000
χ6144-4-24-44-2-4-44220-20222-22i3−2i300−2i32i3-422-24-2-202i3−2i300−2i32i300000000000000000000000000000000000000
χ6244-4-2-24-4-222-2-2-20102-1-11−2i32i34i−4i−2i32i3-21122-1-10i3−i300i3−i323−2300−3−333−2i2i−2i2iii−i−i0000000000000000000000
χ6344-4-2-24-4-222-2-2-20102-1-11−2i32i3−4i4i−2i32i3-21122-1-10i3−i300i3−i3−23230033−3−32i−2i2i−2i−i−iii0000000000000000000000
χ6444-4-2-24-4-222-2-2-20102-1-112i3−2i34i−4i2i3−2i3-21122-1-10−i3i300−i3i3−23230033−3−3−2i2i−2i2iii−i−i0000000000000000000000
χ6544-4-2-24-4-222-2-2-20102-1-112i3−2i3−4i4i2i3−2i3-21122-1-10−i3i300−i3i323−2300−3−3332i−2i2i−2i−i−iii0000000000000000000000
χ6644-4-2-2-44-222-2220102-1-11−2i32i3002i3−2i32-1-1-2-2110i3−i300−i3i300−2i32i3i3−i3−i3i30000-333-30000000000000000000000
χ6744-4-2-2-44-222-2220102-1-11−2i32i3002i3−2i32-1-1-2-2110i3−i300−i3i3002i3−2i3−i3i3i3−i300003-3-330000000000000000000000
χ6844-4-2-2-44-222-2220102-1-112i3−2i300−2i32i32-1-1-2-2110−i3i300i3−i300−2i32i3i3−i3−i3i300003-3-330000000000000000000000
χ6944-4-2-2-44-222-2220102-1-112i3−2i300−2i32i32-1-1-2-2110−i3i300i3−i3002i3−2i3−i3i3i3−i30000-333-30000000000000000000000
χ708-808800-800-800080000-80000000000000000000000000000000000000000000000000000000000
χ718-808-400-8−4i34i34000-400−4i34i340000000000000000000000000000000000000000000000000000000000
χ728-808-400-84i3−4i34000-4004i3−4i340000000000000000000000000000000000000000000000000000000000
χ738-80-4800400-843−430-400004000000043−430000000000000000000000000000000000000000000000000
χ748-80-4800400-8−43430-4000040000000−43430000000000000000000000000000000000000000000000000
χ758-80-4-4004−4i34i3443−4302002i3−2i3-20000000−2323006i−6i000000000000000000000000000000000000000000000
χ768-80-4-4004−4i34i34−434302002i3−2i3-2000000023−2300−6i6i000000000000000000000000000000000000000000000
χ778-80-4-40044i3−4i3443−430200−2i32i3-20000000−232300−6i6i000000000000000000000000000000000000000000000
χ788-80-4-40044i3−4i34−43430200−2i32i3-2000000023−23006i−6i000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.