Finite Group Databasebeta

← Group #10690339

Character table — Group #10690339

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12222222222236666666444466661212121244444444888812121212121212121212242424242424242444441212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ911-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111i−ii−iii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i1-1i−i1-111-1-1ii−i−i
χ1011-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111i−ii−iii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−i-11−ii-11-1-111−i−iii
χ1111-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111i−ii−i−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i1-1i−i1-1-1-111−i−iii
χ1211-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111i−ii−i−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i-11−ii-1111-1-1ii−i−i
χ1311-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111−ii−iiii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii-11i−i-1111-1-1−i−iii
χ1411-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111−ii−iiii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iii1-1−ii1-1-1-111ii−i−i
χ1511-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111−ii−ii−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iii-11i−i-11-1-111ii−i−i
χ1611-11-1-1-1111-1-1111-1-11-1-11-11-111-1-1-1-111−ii−ii−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii1-1−ii1-111-1-1−i−iii
χ1722222222222222222222-2-2-2-22222-2-2-2-2000000000000-2-200000000000000002222000000-2-20000000000
χ1822222222222222222222-2-2-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2-2-2000000220000000000
χ19222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ20222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ21222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2322222222-2-2-2-2222222222-2-22-2-2-2-2-2-2-2-222-2-20000000022000000000000000000002-22-200000000000000
χ2422222222-2-2-2-2222222222-2-22-2-2-2-2-2-2-2-2-2-222000000002200000000000000000000-22-2200000000000000
χ2522222222-2-2-2-222222222-222-2-2-2-2-22222000000000000-2-20000000000000000000000002200-2-200000000
χ2622222222-2-2-2-222222222-222-2-2-2-2-22222000000000000-2-2000000000000000000000000-2-2002200000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-12-2-221111111122-2-200000000-1-133−3−333−3−333−3−333−3−30000-11-1100000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-12-2-221111111122-2-200000000-1-1−3−333−3−333−3−333−3−3330000-11-1100000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-12-2-2211111111-2-22200000000-1-133−3−333−3−3−3−333−3−33300001-11-100000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-12-2-2211111111-2-22200000000-1-1−3−333−3−33333−3−333−3−300001-11-100000000000000
χ3122-22-2-2-2222-2-2222-2-22-2-2-22-2222-2-222-2-2000000000000-2200000000000000002i2i−2i−2i000000−2i2i0000000000
χ3222-22-2-2-2222-2-2222-2-22-2-2-22-2222-2-222-2-2000000000000-220000000000000000−2i−2i2i2i0000002i−2i0000000000
χ3322-22-2-2-2222-2-2-1-1-111-1112-22-2-1-11111-1-12i−2i2i−2i2i2i−2i−2i22-2-2-11−i−i−i−iiiii-1-1-1-111110000−i−iii00000000000000
χ3422-22-2-2-2222-2-2-1-1-111-1112-22-2-1-11111-1-12i−2i2i−2i−2i−2i2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-10000−i−iii00000000000000
χ3522-22-2-2-2222-2-2-1-1-111-1112-22-2-1-11111-1-1−2i2i−2i2i2i2i−2i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-10000ii−i−i00000000000000
χ3622-22-2-2-2222-2-2-1-1-111-1112-22-2-1-11111-1-1−2i2i−2i2i−2i−2i2i2i22-2-2-11iiii−i−i−i−i-1-1-1-111110000ii−i−i00000000000000
χ3722-22-2-2-22-2-222222-2-22-2-222-2-2-2-22222-2-22i−2i−2i2i000000002-2000000000000000000002i−2i−2i2i00000000000000
χ3822-22-2-2-22-2-222222-2-22-2-222-2-2-2-22222-2-2−2i2i2i−2i000000002-200000000000000000000−2i2i2i−2i00000000000000
χ3922-22-2-2-22-2-222222-2-22-2-2-2-222-2-222-2-222000000000000-220000000000000000000000002-200-2200000000
χ4022-22-2-2-22-2-222222-2-22-2-2-2-222-2-222-2-222000000000000-22000000000000000000000000-22002-200000000
χ4122-22-2-2-22-2-222-1-1-111-11122-2-211-1-1-1-1112i−2i−2i2i00000000-11−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000−iii−i00000000000000
χ4222-22-2-2-22-2-222-1-1-111-11122-2-211-1-1-1-1112i−2i−2i2i00000000-11i3i3−i3−i3−i3−i3i3i333−3−3−3−3330000−iii−i00000000000000
χ4322-22-2-2-22-2-222-1-1-111-11122-2-211-1-1-1-111−2i2i2i−2i00000000-11−i3−i3i3i3i3i3−i3−i333−3−3−3−3330000i−i−ii00000000000000
χ4422-22-2-2-22-2-222-1-1-111-11122-2-211-1-1-1-111−2i2i2i−2i00000000-11i3i3−i3−i3−i3−i3i3i3−3−33333−3−30000i−i−ii00000000000000
χ452-22-2-22-222-22-222-222-2-2-200002-22-20000000000002−22−200000000002−22−22−22−22i−2i2i−2i00000000000000−i2i2−i2i2
χ462-22-2-22-222-22-222-222-2-2-200002-22-20000000000002−22−200000000002−22−22−22−2−2i2i−2i2i00000000000000i2−i2i2−i2
χ472-22-2-22-222-22-222-222-2-2-200002-22-2000000000000−22−220000000000−22−22−22−222i−2i2i−2i00000000000000i2−i2i2−i2
χ482-22-2-22-222-22-222-222-2-2-200002-22-2000000000000−22−220000000000−22−22−22−22−2i2i−2i2i00000000000000−i2i2−i2i2
χ492-2-2-22-2222-2-2222-2-2-2-22200002-2-220000000000002−2−2200000000002−22−2−22−222-2-2200000000000000−222−2
χ502-2-2-22-2222-2-2222-2-2-2-22200002-2-220000000000002−2−2200000000002−22−2−22−22-222-2000000000000002−2−22
χ512-2-2-22-2222-2-2222-2-2-2-22200002-2-22000000000000−222−20000000000−22−222−22−22-2-22000000000000002−2−22
χ522-2-2-22-2222-2-2222-2-2-2-22200002-2-22000000000000−222−20000000000−22−222−22−2-222-200000000000000−222−2
χ53444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-4-4-4-4-2-2-2-2-2-2-2-2-444-42222-2-2-2-20000000000002200000000000000000000000000000000000000
χ55444-44-4-4-400004-444-4-44-400000000000000002-22-20000002-22-22-22-2000000000000000000000000000000
χ56444-44-4-4-400004-444-4-44-40000000000000000-22-22000000-22-22-22-22000000000000000000000000000000
χ57444-44-4-4-40000-22-2-222-220000000023−2323−2300002-22-2000000−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000000000
χ58444-44-4-4-40000-22-2-222-220000000023−2323−230000-22-220000001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000000000
χ59444-44-4-4-40000-22-2-222-2200000000−2323−232300002-22-2000000−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000000000
χ60444-44-4-4-40000-22-2-222-2200000000−2323−23230000-22-220000001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000000000
χ6144-44-4-4-4444-4-4-2-2-222-222-44-44-2-222-2-2220000000000002-200000000000000000000000000000000000000
χ6244-44-4-4-44-4-444-2-2-222-222-4-44422-2-222-2-20000000000002-200000000000000000000000000000000000000
χ6344-4-4-444-400004-44-44-4-4400000000000000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ6444-4-4-444-400004-44-44-4-440000000000000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ6544-4-4-444-40000-22-22-222-20000000023−23−232300002i−2i−2i2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000000000
χ6644-4-4-444-40000-22-22-222-20000000023−23−23230000−2i2i2i−2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000000000
χ6744-4-4-444-40000-22-22-222-200000000−232323−2300002i−2i−2i2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000000000
χ6844-4-4-444-40000-22-22-222-200000000−232323−230000−2i2i2i−2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000000000
χ694-444-4-44-400004-4-44-44-44000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ704-444-4-44-400004-4-44-44-4400000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ714-44-4-44-444-44-4-2-22-2-22220000-22-2200000000000022−2222−220000000000−22−22−22−220000000000000000000000
χ724-44-4-44-444-44-4-2-22-2-22220000-22-22000000000000−2222−222200000000002−22−22−22−20000000000000000000000
χ734-44-4-44-44-44-4444-444-4-4-40000-44-4400000000000000000000000000000000000000000000000000000000
χ744-44-4-44-44-44-44-2-22-2-222200002-22-2000000000000000000000000006−6−666−6−660000000000000000000000
χ754-44-4-44-44-44-44-2-22-2-222200002-22-200000000000000000000000000−666−6−666−60000000000000000000000
χ764-4-4444-4-400004-4-4-4444-4000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ774-4-4444-4-400004-4-4-4444-400000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ784-4-4-44-4444-4-44-2-22222-2-20000-222-200000000000022−22−22220000000000−22−222−22−20000000000000000000000
χ794-4-4-44-4444-4-44-2-22222-2-20000-222-2000000000000−222222−2200000000002−22−2−22−220000000000000000000000
χ804-4-4-44-444-444-444-4-4-4-4440000-444-400000000000000000000000000000000000000000000000000000000
χ814-4-4-44-444-444-4-2-22222-2-200002-2-22000000000000000000000000006−6−66−666−60000000000000000000000
χ824-4-4-44-444-444-4-2-22222-2-200002-2-2200000000000000000000000000−666−66−6−660000000000000000000000
χ838-888-8-88-80000-444-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-80000-4444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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