Finite Group Databasebeta

← Group #10868298

Character table — Group #10868298

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order122222223444466666664444121212121212121244444444888812121212121212121212242424242424242444444444121212122444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ511111111111111111111111111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ911111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-1-111-1-1-11
χ1011111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1111-1
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1-11-1-1-1-1111-1
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11111-1-1-11
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-111-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1111-1-1-111-1-11-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-111111-1-11-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1111-1-1-1-1-111-11
χ17222222222-2-2-2-2222222222-2-2-2-22222-2-200000000000000000000-2-200000000220000-2-200002-200000000
χ18222222222-2-2-2-2222222222-2-2-2-22222-2-200000000000000000000-2-200000000-2-20000220000-2200000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000000000002200000000220000220000-2-200000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000000000002200000000-2-20000-2-200002200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-211111111-1-11111111100000000-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000011110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-12222-2-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-222-2-2-2-2221111-1-1-1-1111111-1-1-1-100000000-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-222-2-222-2-222-1-1-1-11111111111-1-1-1-10000000011-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-2-2-2222222-2-21111-1-1-1-111-1-1-1-111110000000011-1-10000000000
χ2922-2-2-22-2222-2-22-22-222-2-22i−2i2i−2i2-22i2i−2i−2i2-22-200002i−2i0000000000002i−2i00000000000000002-22i−2i0000000000
χ3022-2-2-22-2222-2-22-22-222-2-22i−2i2i−2i2-22i2i−2i−2i2-2-220000−2i2i0000000000002i−2i0000000000000000-22−2i2i0000000000
χ3122-2-2-22-2222-2-22-22-222-2-2−2i2i−2i2i2-2−2i−2i2i2i2-22-20000−2i2i000000000000−2i2i00000000000000002-2−2i2i0000000000
χ3222-2-2-22-2222-2-22-22-222-2-2−2i2i−2i2i2-2−2i−2i2i2i2-2-2200002i−2i000000000000−2i2i0000000000000000-222i−2i0000000000
χ3322-2-2-22-222-222-2-22-222-2-22i−2i−2i2i-222i2i−2i−2i-2200000000000000000000−2i2i00000000002i2i−2i−2i000000002-2000000
χ3422-2-2-22-222-222-2-22-222-2-22i−2i−2i2i-222i2i−2i−2i-2200000000000000000000−2i2i0000000000−2i−2i2i2i00000000-22000000
χ3522-2-2-22-222-222-2-22-222-2-2−2i2i2i−2i-22−2i−2i2i2i-22000000000000000000002i−2i00000000002i2i−2i−2i00000000-22000000
χ3622-2-2-22-222-222-2-22-222-2-2−2i2i2i−2i-22−2i−2i2i2i-22000000000000000000002i−2i0000000000−2i−2i2i2i000000002-2000000
χ3722-2-2-22-22-12-2-221-11-1-1112i−2i2i−2i-11−i−iii-112-200002i−2i000033−3−3−i3−i3i3i3−ii33−3−3−i3−i3i3i300000000-11−ii0000000000
χ3822-2-2-22-22-12-2-221-11-1-1112i−2i2i−2i-11−i−iii-112-200002i−2i0000−3−333i3i3−i3−i3−ii−3−333i3i3−i3−i300000000-11−ii0000000000
χ3922-2-2-22-22-12-2-221-11-1-1112i−2i2i−2i-11−i−iii-11-220000−2i2i000033−3−3−i3−i3i3i3−ii−3−333i3i3−i3−i3000000001-1i−i0000000000
χ4022-2-2-22-22-12-2-221-11-1-1112i−2i2i−2i-11−i−iii-11-220000−2i2i0000−3−333i3i3−i3−i3−ii33−3−3−i3−i3i3i3000000001-1i−i0000000000
χ4122-2-2-22-22-12-2-221-11-1-111−2i2i−2i2i-11ii−i−i-112-20000−2i2i000033−3−3i3i3−i3−i3i−i33−3−3i3i3−i3−i300000000-11i−i0000000000
χ4222-2-2-22-22-12-2-221-11-1-111−2i2i−2i2i-11ii−i−i-112-20000−2i2i0000−3−333−i3−i3i3i3i−i−3−333−i3−i3i3i300000000-11i−i0000000000
χ4322-2-2-22-22-12-2-221-11-1-111−2i2i−2i2i-11ii−i−i-11-2200002i−2i000033−3−3i3i3−i3−i3i−i−3−333−i3−i3i3i3000000001-1−ii0000000000
χ4422-2-2-22-22-12-2-221-11-1-111−2i2i−2i2i-11ii−i−i-11-2200002i−2i0000−3−333−i3−i3i3i3i−i33−3−3i3i3−i3−i3000000001-1−ii0000000000
χ452-222-2-2-222-22-2222-2-2-22-20000-2-200002200002i−2i00000000002i−2i2i−2i0000000000002i−2i2i−2i0000000000002-200
χ462-222-2-2-222-22-2222-2-2-22-20000-2-200002200002i−2i00000000002i−2i2i−2i000000000000−2i2i−2i2i000000000000-2200
χ472-222-2-2-222-22-2222-2-2-22-20000-2-20000220000−2i2i0000000000−2i2i−2i2i0000000000002i−2i2i−2i000000000000-2200
χ482-222-2-2-222-22-2222-2-2-22-20000-2-20000220000−2i2i0000000000−2i2i−2i2i000000000000−2i2i−2i2i0000000000002-200
χ492-2-2-22-222222-2-2-222-2-2-2200002-20000-22002i−2i000000002i−2i2i−2i00000000000000002-2-2200000000002i−2i0000
χ502-2-2-22-222222-2-2-222-2-2-2200002-20000-22002i−2i000000002i−2i2i−2i0000000000000000-222-20000000000−2i2i0000
χ512-2-2-22-222222-2-2-222-2-2-2200002-20000-2200−2i2i00000000−2i2i−2i2i00000000000000002-2-220000000000−2i2i0000
χ522-2-2-22-222222-2-2-222-2-2-2200002-20000-2200−2i2i00000000−2i2i−2i2i0000000000000000-222-200000000002i−2i0000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422-2-2-2-2220000000000000000000022000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4442222222200000000000000000000-2-2000000000000000000000000000000
χ55444-44-4-4-4400004-444-4-4-40000000000000000000000000000000000000000004-400000000000000000000
χ56444-44-4-4-4400004-444-4-4-4000000000000000000000000000000000000000000-4400000000000000000000
χ5744-44-4-44-440000-4-4-44-4440000000000000000000000000000000000000000000000004i−4i00000000000000
χ5844-44-4-44-440000-4-4-44-444000000000000000000000000000000000000000000000000−4i4i00000000000000
χ5944-4-4-44-44-2-444-42-22-2-2224i−4i−4i4i2-2−2i−2i2i2i2-2000000000000000000002i−2i000000000000000000000000000000
χ6044-4-4-44-44-2-444-42-22-2-222−4i4i4i−4i2-22i2i−2i−2i2-200000000000000000000−2i2i000000000000000000000000000000
χ614-444-4-4-4444-44-444-4-4-44-40000440000-4-40000000000000000000000000000000000000000000000000000
χ624-444-4-4-44-24-44-4-2-2222-220000-2-2000022000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ634-444-4-4-44-24-44-4-2-2222-220000-2-20000220000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ644-444-4-4-44-2-44-44-2-2222-220000220000-2-200004i−4i0000000000−2i2i−2i2i00000000000000000000000000000000
χ654-444-4-4-44-2-44-44-2-2222-220000220000-2-20000−4i4i00000000002i−2i2i−2i00000000000000000000000000000000
χ664-44-4-444-4400004-4-4-44-440000000000000000000000−2i22i200000000000000−2i22i2−2i22i20000000000000000000000
χ674-44-4-444-4400004-4-4-44-4400000000000000000000002i2−2i2000000000000002i2−2i22i2−2i20000000000000000000000
χ684-44-4-444-4-20000-2222-22-200000023−2323−23000000000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i20000000000000000000000
χ694-44-4-444-4-20000-2222-22-200000023−2323−230000000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i20000000000000000000000
χ704-44-4-444-4-20000-2222-22-2000000−2323−2323000000000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i20000000000000000000000
χ714-44-4-444-4-20000-2222-22-2000000−2323−23230000000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i20000000000000000000000
χ724-4-4444-4-440000-4-44-444-400000000000000000000−2i22i2000000000000−2i22i22i2−2i200000000000000000000000000
χ734-4-4444-4-440000-4-44-444-4000000000000000000002i2−2i20000000000002i2−2i2−2i22i200000000000000000000000000
χ744-4-4444-4-4-2000022-22-2-22000000−2i32i32i3−2i30000000000−2i22i2000000000000i2−i2−i2i26−6−660000000000000000000000
χ754-4-4444-4-4-2000022-22-2-22000000−2i32i32i3−2i300000000002i2−2i2000000000000−i2i2i2−i2−666−60000000000000000000000
χ764-4-4444-4-4-2000022-22-2-220000002i3−2i3−2i32i30000000000−2i22i2000000000000i2−i2−i2i2−666−60000000000000000000000
χ774-4-4444-4-4-2000022-22-2-220000002i3−2i3−2i32i300000000002i2−2i2000000000000−i2i2i2−i26−6−660000000000000000000000
χ784-4-4-44-4444-4-444-444-4-4-440000-4400004-40000000000000000000000000000000000000000000000000000
χ794-4-4-44-444-244-4-42-2-2222-20000-2200002-2004i−4i00000000−2i2i−2i2i000000000000000000000000000000000000
χ804-4-4-44-444-244-4-42-2-2222-20000-2200002-200−4i4i000000002i−2i2i−2i000000000000000000000000000000000000
χ814-4-4-44-444-2-4-4442-2-2222-200002-20000-22000000000000000023−23−232300000000000000000000000000000000
χ824-4-4-44-444-2-4-4442-2-2222-200002-20000-220000000000000000−232323−2300000000000000000000000000000000
χ83888-88-8-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-88-8-40000444-44-4-40000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).