Finite Group Databasebeta

← Group #10690340

Character table — Group #10690340

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order122222222222366666664444666612121212224444448888121212121212121212122424242424242424444466121244444444448888
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
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-1111-11-111-1-111-1-11-11111-1-1-1-11111-1-1-1-1ii−i−i1-11-1i−ii−ii−iii−i−iii−i−i
χ1011-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-1111-11-111-1-111-1-11-11111-1-1-1-11111-1-1-1-1−i−iii1-11-1−ii−ii−ii−i−iii−i−iii
χ1111-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-11111ii−i−i1-11-1i−ii−ii−i−i−iii−i−iii
χ1211-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-11111−i−iii1-11-1−ii−ii−iiii−i−iii−i−i
χ1311-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111ii−i−i-11-11i−i−ii−iiii−i−i−i−iii
χ1411-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111−i−iii-11-11−iii−ii−i−i−iiiii−i−i
χ1511-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-111-11-11-1-11111-1-11-1-1-1-1-111111111-1-1-1-1ii−i−i-11-11i−i−ii−ii−i−iiiii−i−i
χ1611-111-1-1-111-1-111-1-1-1-1111-11-111-1-1-1-111-11-11-1-11111-1-11-1-1-1-1-111111111-1-1-1-1−i−iii-11-11−iii−ii−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-22222-2-2-2-2000000000000-2-2000000000000000022220000-2-2000000000000
χ1822222222222222222222-2-2-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2-2-2000022000000000000
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
χ2322222222-2-2-2-2222222222-2-22-2-2-2-2-2-2-2-2000000000000220000000000000000000000000022-2-200000000
χ2422222222-2-2-2-2222222222-2-22-2-2-2-2-2-2-2-20000000000002200000000000000000000000000-2-22200000000
χ2522222222-2-2-2-222222222-222-2-2-2-2-2222222-2-200000000-2-20000000000000000000022-2-200000000000000
χ2622222222-2-2-2-222222222-222-2-2-2-2-22222-2-22200000000-2-200000000000000000000-2-22200000000000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-1-222-21111-1-1-1-122-2-20000000011−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000-1-11100000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-1-222-21111-1-1-1-122-2-20000000011i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000-1-11100000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-1-222-21111-1-1-1-1-2-2220000000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000011-1-100000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-1-222-21111-1-1-1-1-2-2220000000011i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000011-1-100000000000000
χ3122-222-2-2-222-2-222-2-2-2-222-22-2222-2-222-2-2000000000000-2200000000000000002i2i−2i−2i0000−2i2i000000000000
χ3222-222-2-2-222-2-222-2-2-2-222-22-2222-2-222-2-2000000000000-220000000000000000−2i−2i2i2i00002i−2i000000000000
χ3322-222-2-2-222-2-2-1-11111-1-12-22-2-1-11111-1-12-22-222-2-222-2-2-11-1-1-1-11111-1-1-1-111110000-11-1100000000000000
χ3422-222-2-2-222-2-2-1-11111-1-12-22-2-1-11111-1-12-22-2-2-222-2-222-111111-1-1-1-11111-1-1-1-10000-11-1100000000000000
χ3522-222-2-2-222-2-2-1-11111-1-12-22-2-1-11111-1-1-22-2222-2-2-2-222-11-1-1-1-111111111-1-1-1-100001-11-100000000000000
χ3622-222-2-2-222-2-2-1-11111-1-12-22-2-1-11111-1-1-22-22-2-22222-2-2-111111-1-1-1-1-1-1-1-1111100001-11-100000000000000
χ3722-222-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-20000000000002-2000000000000000000000000002i−2i−2i2i00000000
χ3822-222-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-20000000000002-200000000000000000000000000−2i2i2i−2i00000000
χ3922-222-2-2-2-2-22222-2-2-2-222-2-222-2-222-2-2222-2-2200000000-22000000000000000000002-2-2200000000000000
χ4022-222-2-2-2-2-22222-2-2-2-222-2-222-2-222-2-222-222-200000000-2200000000000000000000-222-200000000000000
χ4122-222-2-2-2-2-222-1-11111-1-1-2-22211-1-111-1-12-2-22000000001-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000-111-100000000000000
χ4222-222-2-2-2-2-222-1-11111-1-1-2-22211-1-111-1-12-2-22000000001-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000-111-100000000000000
χ4322-222-2-2-2-2-222-1-11111-1-1-2-22211-1-111-1-1-222-2000000001-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300001-1-1100000000000000
χ4422-222-2-2-2-2-222-1-11111-1-1-2-22211-1-111-1-1-222-2000000001-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300001-1-1100000000000000
χ452-22-222-2-22-22-22-222-2-2-2200002-22-20000000000002−22−200000000002−22−22−22−22i−2i2i−2i00000000000000−i2i2−i2i2
χ462-22-222-2-22-22-22-222-2-2-2200002-22-20000000000002−22−200000000002−22−22−22−2−2i2i−2i2i00000000000000i2−i2i2−i2
χ472-22-222-2-22-22-22-222-2-2-2200002-22-2000000000000−22−220000000000−22−22−22−222i−2i2i−2i00000000000000i2−i2i2−i2
χ482-22-222-2-22-22-22-222-2-2-2200002-22-2000000000000−22−220000000000−22−22−22−22−2i2i−2i2i00000000000000−i2i2−i2i2
χ492-2-2-22-2222-2-222-2-2-222-2200002-2-220000000000002−2−2200000000002−22−2−22−222-2-2200000000000000−222−2
χ502-2-2-22-2222-2-222-2-2-222-2200002-2-220000000000002−2−2200000000002−22−2−22−22-222-2000000000000002−2−22
χ512-2-2-22-2222-2-222-2-2-222-2200002-2-22000000000000−222−20000000000−22−222−22−22-2-22000000000000002−2−22
χ522-2-2-22-2222-2-222-2-2-222-2200002-2-22000000000000−222−20000000000−22−222−22−2-222-200000000000000−222−2
χ53444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-4-4-4-4-2-2-2-2-2-2-2-24-4-4422222222000000000000-2-200000000000000000000000000000000000000
χ55444-4-4-44-40000444-44-4-4-4000000000000000000000000000000000000000000000000000000002-22-20000
χ56444-4-4-44-40000444-44-4-4-400000000000000000000000000000000000000000000000000000000-22-220000
χ5744-444-4-4-444-4-4-2-22222-2-2-44-44-2-222-2-2220000000000002-200000000000000000000000000000000000000
χ5844-444-4-4-4-4-444-2-22222-2-244-4-422-2-2-2-222000000000000-2200000000000000000000000000000000000000
χ5944-4-4-44-44000044-44-44-4-4000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ6044-4-4-44-44000044-44-44-4-400000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ614-444-4-4-4400004-44-4-444-400000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ624-444-4-4-4400004-44-4-444-40000000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ634-444-4-4-440000-22-222-2-2200000000−2i32i3−2i32i300002i−2i2i−2i0000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000000000
χ644-444-4-4-440000-22-222-2-2200000000−2i32i3−2i32i30000−2i2i−2i2i000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000000000
χ654-444-4-4-440000-22-222-2-22000000002i3−2i32i3−2i300002i−2i2i−2i0000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000000000
χ664-444-4-4-440000-22-222-2-22000000002i3−2i32i3−2i30000−2i2i−2i2i000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000000000
χ674-44-444-4-44-44-4-22-2-2222-20000-22-2200000000000022−2222−220000000000−22−22−22−220000000000000000000000
χ684-44-444-4-44-44-4-22-2-2222-20000-22-22000000000000−2222−222200000000002−22−22−22−20000000000000000000000
χ694-44-444-4-4-44-444-444-4-4-440000-44-4400000000000000000000000000000000000000000000000000000000
χ704-44-444-4-4-44-44-22-2-2222-200002-22-200000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ714-44-444-4-4-44-44-22-2-2222-200002-22-200000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ724-4-44-444-400004-4-444-44-400000000000000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-4-44-444-400004-4-444-44-40000000000000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ744-4-44-444-40000-222-2-22-2200000000−2i32i32i3−2i300002i−2i−2i2i0000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000000000
χ754-4-44-444-40000-222-2-22-2200000000−2i32i32i3−2i30000−2i2i2i−2i000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000000000
χ764-4-44-444-40000-222-2-22-22000000002i3−2i3−2i32i300002i−2i−2i2i0000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000000000
χ774-4-44-444-40000-222-2-22-22000000002i3−2i3−2i32i30000−2i2i2i−2i000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000000000
χ784-4-4-44-4444-4-44-2222-2-22-20000-222-200000000000022−22−22220000000000−22−222−22−20000000000000000000000
χ794-4-4-44-4444-4-44-2222-2-22-20000-222-2000000000000−222222−2200000000002−22−2−22−220000000000000000000000
χ804-4-4-44-444-444-44-4-4-444-440000-444-400000000000000000000000000000000000000000000000000000000
χ814-4-4-44-444-444-4-2222-2-22-200002-2-2200000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ824-4-4-44-444-444-4-2222-2-22-200002-2-2200000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ83888-8-8-88-80000-4-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-880000-4-44-44-4440000000000000000000000000000000000000000000000000000000000000000

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