Finite Group Databasebeta

← Group #10867987

Character table — Group #10867987

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order12222222344446666666448888121212124444222444466881212242424242424242444444444888846612121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1111-1-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-111-1-111-1
χ911111111111111111111-1-1111111111111-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111111-111-1-1-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-11111-1-1-111-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-11111-1-11-1-11111-1
χ1311111111111111111111-1-1-1-1-1-111111111-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1111111111-1-1-1-111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-22222-2000000-2-2002200000000-2-22200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2000000-2-200220000000022-2-20000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2222220000002200-2-200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000002200-2-200000000222200000000000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002222222-1-122-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-1-1-2-2-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-2-2-222-1-1-2-2-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-222-2-22211-2-211-1-1-1-11111000000000000-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-222-2-211-2-211-1-1-1-11111000000000000211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-222-2-2-2-21122111111-1-1-1-10000000000002-1-1-1-1111100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222221122111111-1-1-1-1000000000000-21111-1-1-1-100000000
χ29222-2-22-2-22-2-22222-2-22-2-20000002-22-20000000002i−2i0000000000000000002i2i−2i−2i22-2-200000002i−2i00000000
χ30222-2-22-2-22-2-22222-2-22-2-20000002-22-20000000002i−2i000000000000000000−2i−2i2i2i-2-22200000002i−2i00000000
χ31222-2-22-2-22-2-22222-2-22-2-20000002-22-2000000000−2i2i0000000000000000002i2i−2i−2i-2-2220000000−2i2i00000000
χ32222-2-22-2-22-2-22222-2-22-2-20000002-22-2000000000−2i2i000000000000000000−2i−2i2i2i22-2-20000000−2i2i00000000
χ3322-222-2-2-222-2-22-2-22-22-22000000-222-22i2i−2i−2i0002-200000000000000002i−2i0000000000000002-20002i−2i00000
χ3422-222-2-2-222-2-22-2-22-22-22000000-222-22i2i−2i−2i000-2200000000000000002i−2i000000000000000-22000−2i2i00000
χ3522-222-2-2-222-2-22-2-22-22-22000000-222-2−2i−2i2i2i0002-20000000000000000−2i2i0000000000000002-2000−2i2i00000
χ3622-222-2-2-222-2-22-2-22-22-22000000-222-2−2i−2i2i2i000-220000000000000000−2i2i000000000000000-220002i−2i00000
χ3722-222-2-2-22-222-2-2-22-22-220000002-2-222i2i−2i−2i02-2000000000000000000−2i2i002i−2i2i−2i000002-200000000000000
χ3822-222-2-2-22-222-2-2-22-22-220000002-2-222i2i−2i−2i0-22000000000000000000−2i2i00−2i2i−2i2i00000-2200000000000000
χ3922-222-2-2-22-222-2-2-22-22-220000002-2-22−2i−2i2i2i02-20000000000000000002i−2i00−2i2i−2i2i000002-200000000000000
χ4022-222-2-2-22-222-2-2-22-22-220000002-2-22−2i−2i2i2i0-220000000000000000002i−2i002i−2i2i−2i00000-2200000000000000
χ4122-2-2-2-22222-22-2-2-2-2222-2002i2i−2i−2i22-2-2000000000000000002i2i−2i−2i000000002-2-2200000000000000002i−2i000
χ4222-2-2-2-22222-22-2-2-2-2222-2002i2i−2i−2i22-2-2000000000000000002i2i−2i−2i00000000-222-20000000000000000−2i2i000
χ4322-2-2-2-22222-22-2-2-2-2222-200−2i−2i2i2i22-2-200000000000000000−2i−2i2i2i000000002-2-220000000000000000−2i2i000
χ4422-2-2-2-22222-22-2-2-2-2222-200−2i−2i2i2i22-2-200000000000000000−2i−2i2i2i00000000-222-200000000000000002i−2i000
χ452-22-22-2-22200002-22-2-22-22i−2i−i2i2−i2i200002-22-20000000002−22i−2i−i2i2−i2i222−2−2002i−2i0000−i2i2−i2i2000000000000002−20
χ462-22-22-2-22200002-22-2-22-22i−2i−i2i2−i2i20000-22-220000000002−22i−2i−i2i2−i2i222−2−200−2i2i0000i2−i2i2−i200000000000000−220
χ472-22-22-2-22200002-22-2-22-22i−2ii2−i2i2−i200002-22-2000000000−222i−2ii2−i2i2−i2−2−222002i−2i0000i2−i2i2−i200000000000000−220
χ482-22-22-2-22200002-22-2-22-22i−2ii2−i2i2−i20000-22-22000000000−222i−2ii2−i2i2−i2−2−22200−2i2i0000−i2i2−i2i2000000000000002−20
χ492-22-22-2-22200002-22-2-22-2−2i2i−i2i2−i2i200002-22-2000000000−22−2i2i−i2i2−i2i2−2−22200−2i2i0000−i2i2−i2i200000000000000−220
χ502-22-22-2-22200002-22-2-22-2−2i2i−i2i2−i2i20000-22-22000000000−22−2i2i−i2i2−i2i2−2−222002i−2i0000i2−i2i2−i2000000000000002−20
χ512-22-22-2-22200002-22-2-22-2−2i2ii2−i2i2−i200002-22-20000000002−2−2i2ii2−i2i2−i222−2−200−2i2i0000i2−i2i2−i2000000000000002−20
χ522-22-22-2-22200002-22-2-22-2−2i2ii2−i2i2−i20000-22-220000000002−2−2i2ii2−i2i2−i222−2−2002i−2i0000−i2i2−i2i200000000000000−220
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000-40000002200-2-20000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000222200004000000-2-200220000000000000000000000000000000000000
χ55444-4-44-4-4444-4-444-4-44-4-4000000-44-44000000000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-244-4-4-2-222-2220000002-22-2000000000000000000000000000000000000000023−23000000000000
χ57444-4-44-4-4-244-4-4-2-222-2220000002-22-20000000000000000000000000000000000000000−2323000000000000
χ58444-4-44-4-4-2-4-444-2-222-222000000-22-220000000004i−4i000000000000000000000000000000000−2i2i00000000
χ59444-4-44-4-4-2-4-444-2-222-222000000-22-22000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ6044-444-4-4-4-24-4-4422-22-22-20000002-2-2200000004-4000000000000000000000000000000000-220000000000
χ6144-444-4-4-4-24-4-4422-22-22-20000002-2-220000000-440000000000000000000000000000000002-20000000000
χ6244-444-4-4-4-2-444-422-22-22-2000000-222-2000004-40000000000000000000000000000000-2200000000000000
χ6344-444-4-4-4-2-444-422-22-22-2000000-222-200000-4400000000000000000000000000000002-200000000000000
χ6444-4-4-4-4444-44-44-4-4-4444-4000000-4-444000000000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-24-44-4222-2-2-22004i4i−4i−4i-2-22200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ6644-4-4-4-444-24-44-4222-2-2-2200−4i−4i4i4i-2-222000000000000000002i2i−2i−2i000000000000000000000000000000000
χ6744-4-4-4-444-2-44-44222-2-2-2200000022-2-2000000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ6844-4-4-4-444-2-44-44222-2-2-2200000022-2-20000000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ694-444-4-44-4400004-4-44-4-440000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ704-444-4-44-4400004-4-44-4-4400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ714-44-44-4-44-20000-22-222-224i−4i−2i22i2−2i22i20000000000000000022−22−2i2ii2−i2i2−i2−2−22200000000000000000000000000000
χ724-44-44-4-44-20000-22-222-224i−4i2i2−2i22i2−2i200000000000000000−2222−2i2i−i2i2−i2i222−2−200000000000000000000000000000
χ734-44-44-4-44-20000-22-222-22−4i4i−2i22i2−2i22i200000000000000000−22222i−2ii2−i2i2−i222−2−200000000000000000000000000000
χ744-44-44-4-44-20000-22-222-22−4i4i2i2−2i22i2−2i20000000000000000022−222i−2i−i2i2−i2i2−2−22200000000000000000000000000000
χ754-4-44-44-4440000-44-4-4-4440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ764-4-44-44-4440000-44-4-4-44400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ774-4-44-44-44-200002-2222-2-20022−22−2222000000000000000−2i32i30000−222−2i6−i6−i6i600000000000000000000000000000
χ784-4-44-44-44-200002-2222-2-20022−22−22220000000000000002i3−2i30000−222−2−i6i6i6−i600000000000000000000000000000
χ794-4-44-44-44-200002-2222-2-200−222222−22000000000000000−2i32i300002−2−22−i6i6i6−i600000000000000000000000000000
χ804-4-44-44-44-200002-2222-2-200−222222−220000000000000002i3−2i300002−2−22i6−i6−i6i600000000000000000000000000000
χ814-4-4-4444-440000-4444-4-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ824-4-4-4444-440000-4444-4-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ838-888-8-88-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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