Finite Group Databasebeta

← Group #10691100

Character table — Group #10691100

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446661212121244444446612121212121244888812121212121212121212242424242424242444448824242424444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111-1-111-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-11-1ii−i−iii−i−i1-1
χ101111-1-111-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-1-11−i−iii−i−iii-11
χ111111-1-111-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-1111-1ii−i−i−i−iii-11
χ121111-1-111-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-111-11−i−iiiii−i−i1-1
χ131111-1-111-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1−iiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-1111-1−i−iiiii−i−i-11
χ141111-1-111-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1−iiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-111-11ii−i−i−i−iii1-1
χ151111-1-111-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1−ii−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-11-1−i−iii−i−iii1-1
χ161111-1-111-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1−ii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-1-11ii−i−iii−i−i-11
χ1722222222222-2-22222222-2-20000-22222-2-2-2-2000000-2-200000000000000002222000000-2-20000000000
χ1822222222222-2-22222222-2-20000-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000220000000000
χ192222222-2-2-2-222222-2-2-2-22-22222-222-2-222-2-2-2-200002-222-2-222-2-2000000000000000000000000000000
χ202222222-2-2-2-222222-2-2-2-22-2-2-2-2-2-222-2-222-2-22200002-2-2-222-2-222000000000000000000000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-220000222-2-2-2-222000000-2200000000000000000000000000002-22-2000000
χ222222222-2-2-2-2-2-2222-2-2-2-2-220000222-2-2-2-222000000-220000000000000000000000000000-22-22000000
χ23222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ27222222-1-2-2-2-222-1-1-111112-22222-2-1-111-1-111-2-20000-11-1-111-1-11133−3−333−3−30000003−33−3000000000000
χ28222222-1-2-2-2-222-1-1-111112-22222-2-1-111-1-111-2-20000-11-1-111-1-111−3−333−3−333000000−33−33000000000000
χ29222222-1-2-2-2-222-1-1-111112-2-2-2-2-2-2-1-111-1-111220000-1111-1-111-1-133−3−333−3−3000000−33−33000000000000
χ30222222-1-2-2-2-222-1-1-111112-2-2-2-2-2-2-1-111-1-111220000-1111-1-111-1-1−3−333−3−3330000003−33−3000000000000
χ312222-2-222-2-22222222222-2-200002-2-2-2-22222000000-2-2000000000000000022-2-2000000-220000000000
χ322222-2-222-2-22222222222-2-200002-2-2-2-22222000000-2-20000000000000000-2-2220000002-20000000000
χ332222-2-22-222-222222-2-2-2-2-220000-2-2-22222-2-2000000-2200000000000000000000000000002i−2i−2i2i000000
χ342222-2-22-222-222222-2-2-2-2-220000-2-2-22222-2-2000000-220000000000000000000000000000−2i2i2i−2i000000
χ352222-2-22-222-2-2-2222-2-2-2-22-22i2i−2i−2i2-2-222-2-222−2i2i00002-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ362222-2-22-222-2-2-2222-2-2-2-22-2−2i−2i2i2i2-2-222-2-2222i−2i00002-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ372222-2-2-12-2-22-2-2-1-1-1-1-1-1-1222i2i−2i−2i-2111111112i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ382222-2-2-12-2-22-2-2-1-1-1-1-1-1-1222i2i−2i−2i-2111111112i−2i−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ392222-2-2-12-2-22-2-2-1-1-1-1-1-1-122−2i−2i2i2i-211111111−2i2i2i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ402222-2-2-12-2-22-2-2-1-1-1-1-1-1-122−2i−2i2i2i-211111111−2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ412222-2-2-1-222-2-2-2-1-1-111112-22i2i−2i−2i211-1-111-1-1−2i2i0000-11−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000−333−3000000000000
χ422222-2-2-1-222-2-2-2-1-1-111112-22i2i−2i−2i211-1-111-1-1−2i2i0000-11−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000003−3−33000000000000
χ432222-2-2-1-222-2-2-2-1-1-111112-2−2i−2i2i2i211-1-111-1-12i−2i0000-11ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000003−3−33000000000000
χ442222-2-2-1-222-2-2-2-1-1-111112-2−2i−2i2i2i211-1-111-1-12i−2i0000-11ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000−333−3000000000000
χ4522-2-22-2222-2-2002-2-222-2-200000002-22-20000002−22−200000000002−22−22−22−22-22-20000000000002−22−200
χ4622-2-22-2222-2-2002-2-222-2-200000002-22-20000002−22−200000000002−22−22−22−2-22-22000000000000−22−2200
χ4722-2-22-2222-2-2002-2-222-2-200000002-22-2000000−22−220000000000−22−22−22−222-22-2000000000000−22−2200
χ4822-2-22-2222-2-2002-2-222-2-200000002-22-2000000−22−220000000000−22−22−22−22-22-220000000000002−22−200
χ4922-2-2-2222-22-2002-2-222-2-20000000-22-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22-2-22000000000000−i2i2i2−i200
χ5022-2-2-2222-22-2002-2-222-2-20000000-22-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2-222-2000000000000i2−i2−i2i200
χ5122-2-2-2222-22-2002-2-222-2-20000000-22-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22-2-22000000000000i2−i2−i2i200
χ5222-2-2-2222-22-2002-2-222-2-20000000-22-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2-222-2000000000000−i2i2i2−i200
χ53444444-24444-4-4-2-2-2-2-2-2-2-4-40000-4-2-2-2-222220000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-22222-4400004-2-22222-2-20000002-200000000000000000000000000000000000000
χ554444-4-4-24-4-4444-2-2-2-2-2-2-2-4-4000042222-2-2-2-20000002200000000000000000000000000000000000000
χ564444-4-4-2-444-444-2-2-22222-440000-422-2-2-2-2220000002-200000000000000000000000000000000000000
χ5744-4-44-44-4-444004-4-4-4-44400000004-4-4400000000000000000000000000000000000000000000000000
χ5844-4-44-4-244-4-400-222-2-2220000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000
χ5944-4-44-4-244-4-400-222-2-2220000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000
χ6044-4-44-4-2-4-44400-22222-2-20000000-222-2000000000000000000006−6−666−6−660000000000000000000000
χ6144-4-44-4-2-4-44400-22222-2-20000000-222-200000000000000000000−666−6−666−60000000000000000000000
χ6244-4-4-444-44-44004-4-4-4-4440000000-444-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-24-44-400-222-2-22200000002-22-2000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ6444-4-4-44-24-44-400-222-2-22200000002-22-20000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ6544-4-4-44-2-44-4400-22222-2-200000002-2-2200000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ6644-4-4-44-2-44-4400-22222-2-200000002-2-2200000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ674-4-4400400004i−4i-44-40000002+2i−2−2i2−2i−2+2i000004i−4i00000000002+2i−2−2i002−2i−2+2i00000000000000000000000000000000
χ684-4-4400400004i−4i-44-4000000−2−2i2+2i−2+2i2−2i000004i−4i0000000000−2−2i2+2i00−2+2i2−2i00000000000000000000000000000000
χ694-4-440040000−4i4i-44-40000002−2i−2+2i2+2i−2−2i00000−4i4i00000000002−2i−2+2i002+2i−2−2i00000000000000000000000000000000
χ704-4-440040000−4i4i-44-4000000−2+2i2−2i−2−2i2+2i00000−4i4i0000000000−2+2i2−2i00−2−2i2+2i00000000000000000000000000000000
χ714-4-4400-200004i−4i2-2223−2323−23002+2i−2−2i2−2i−2+2i00000−2i2i−2i32i300000000−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000000000
χ724-4-4400-200004i−4i2-2223−2323−2300−2−2i2+2i−2+2i2−2i00000−2i2i−2i32i3000000001+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000000000
χ734-4-4400-200004i−4i2-22−2323−2323002+2i−2−2i2−2i−2+2i00000−2i2i2i3−2i300000000−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000000000
χ744-4-4400-200004i−4i2-22−2323−232300−2−2i2+2i−2+2i2−2i00000−2i2i2i3−2i3000000001+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000000000
χ754-4-4400-20000−4i4i2-2223−2323−23002−2i−2+2i2+2i−2−2i000002i−2i2i3−2i300000000−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000000000
χ764-4-4400-20000−4i4i2-2223−2323−2300−2+2i2−2i−2−2i2+2i000002i−2i2i3−2i3000000001−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000000000
χ774-4-4400-20000−4i4i2-22−2323−2323002−2i−2+2i2+2i−2−2i000002i−2i−2i32i300000000−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000000000
χ784-4-4400-20000−4i4i2-22−2323−232300−2+2i2−2i−2−2i2+2i000002i−2i−2i32i3000000001−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000000000
χ798-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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