Finite Group Databasebeta

← Group #10855217

Character table — Group #10855217

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order12222222344446666666448888121212124444224444488121212122424242424242424222244448888266661212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11-1-111-1-11
χ61111111111111111111111-1-1-1-111111111-1-111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-111111
χ911111111111111111111-1-111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-11-1-11111-1
χ1311111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-1-1111111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-111-1-111-1-11-1-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-1-111-1-11111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-222220000-2000022-2-200000000000022-2-20000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-20000-2000022-2-2000000000000-2-222000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222000020000-2-222000000000000-2-2-2-2000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000-2-22200000000000022220000000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022-2-22-2-2-2-2-1-1-1-1111111110000000000002-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222222-2-2-1-1-1-111111111000000000000-21111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-222-2-21111-1-1-1-11111000000000000-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-222-2-2-2-2-21111-1-1-1-11111000000000000211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-100002222-2-2-22211111111-1-1-1-1000000000000-2-1-111-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-2-2-2222211111111-1-1-1-1000000000000211-1-111-1-100000000
χ29222-2-22-2-22-22-2222-22-2-2-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i000022-2-2000000000000000000002i−2i000
χ30222-2-22-2-22-22-2222-22-2-2-2002i2i−2i−2i2-22-2000000000000000002i2i−2i−2i0000-2-22200000000000000000000−2i2i000
χ31222-2-22-2-22-22-2222-22-2-2-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i000022-2-200000000000000000000−2i2i000
χ32222-2-22-2-22-22-2222-22-2-2-200−2i−2i2i2i2-22-200000000000000000−2i−2i2i2i0000-2-222000000000000000000002i−2i000
χ3322-22-2-22-2200002-22-22-2-22-2−i2i2−i2i200002i2i−2i−2i0000000−i2i22-200−i2i2−i2i2−i2−i2i2i200002i−2i0022−2−2000000000000002−20
χ3422-22-2-22-2200002-22-22-2-22-2−i2i2−i2i20000−2i−2i2i2i0000000−i2i22-200−i2i2−i2i2−i2−i2i2i20000−2i2i00−2−22200000000000000−220
χ3522-22-2-22-2200002-22-22-2-22-2i2−i2i2−i200002i2i−2i−2i0000000i2−i22-200i2−i2i2−i2i2i2−i2−i200002i−2i00−2−22200000000000000−220
χ3622-22-2-22-2200002-22-22-2-22-2i2−i2i2−i20000−2i−2i2i2i0000000i2−i22-200i2−i2i2−i2i2i2−i2−i20000−2i2i0022−2−2000000000000002−20
χ3722-22-2-22-2200002-22-22-2-2-22−i2i2−i2i200002i2i−2i−2i0000000i2−i2-2200−i2i2−i2i2i2i2−i2−i20000−2i2i0022−2−200000000000000−220
χ3822-22-2-22-2200002-22-22-2-2-22−i2i2−i2i20000−2i−2i2i2i0000000i2−i2-2200−i2i2−i2i2i2i2−i2−i200002i−2i00−2−222000000000000002−20
χ3922-22-2-22-2200002-22-22-2-2-22i2−i2i2−i200002i2i−2i−2i0000000−i2i2-2200i2−i2i2−i2−i2−i2i2i20000−2i2i00−2−222000000000000002−20
χ4022-22-2-22-2200002-22-22-2-2-22i2−i2i2−i20000−2i−2i2i2i0000000−i2i2-2200i2−i2i2−i2−i2−i2i2i200002i−2i0022−2−200000000000000−220
χ412-2222-2-2-222-2-22-2-222-22-200000022-2-22i−2i2i−2i000002i−2i000000000000002-22-2002i−2i000000000002i−2i00000000
χ422-2222-2-2-222-2-22-2-222-22-200000022-2-22i−2i2i−2i00000−2i2i00000000000000-22-22002i−2i00000000000−2i2i00000000
χ432-2222-2-2-222-2-22-2-222-22-200000022-2-2−2i2i−2i2i000002i−2i00000000000000-22-2200−2i2i000000000002i−2i00000000
χ442-2222-2-2-222-2-22-2-222-22-200000022-2-2−2i2i−2i2i00000−2i2i000000000000002-22-200−2i2i00000000000−2i2i00000000
χ452-2222-2-2-22-222-2-2-222-22-2000000-2-2222i−2i2i−2i002-200000000000000000000000−2i2i0000000002-20002i−2i00000
χ462-2222-2-2-22-222-2-2-222-22-2000000-2-2222i−2i2i−2i00-2200000000000000000000000−2i2i000000000-22000−2i2i00000
χ472-2222-2-2-22-222-2-2-222-22-2000000-2-222−2i2i−2i2i002-2000000000000000000000002i−2i0000000002-2000−2i2i00000
χ482-2222-2-2-22-222-2-2-222-22-2000000-2-222−2i2i−2i2i00-22000000000000000000000002i−2i000000000-220002i−2i00000
χ492-22-2-2-2222-2-222-2-2-222-220000002-2-2200002-200000000000000000002-2-2200002-22-202-200000000000000
χ502-22-2-2-2222-2-222-2-2-222-220000002-2-2200002-20000000000000000000-222-20000-22-2202-200000000000000
χ512-22-2-2-2222-2-222-2-2-222-220000002-2-220000-2200000000000000000002-2-220000-22-220-2200000000000000
χ522-22-2-2-2222-2-222-2-2-222-220000002-2-220000-220000000000000000000-222-200002-22-20-2200000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222200000000-40000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000004000022-2-20000000000000000000000000000000000000
χ55444-4-44-4-444-44-444-44-4-4-4000000-44-44000000000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-24-44-4-2-22-22220000002-22-200000000000000000000023−2323−2300000000000000000000000000000
χ57444-4-44-4-4-24-44-4-2-22-22220000002-22-2000000000000000000000−2323−232300000000000000000000000000000
χ58444-4-44-4-4-2-44-44-2-22-2222004i4i−4i−4i-22-2200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ59444-4-44-4-4-2-44-44-2-22-222200−4i−4i4i4i-22-22000000000000000002i2i−2i−2i000000000000000000000000000000000
χ6044-44-4-44-4-20000-22-22-2224-4−2i22i2−2i22i2000000000000000−2i22i2-2200i2−i2i2−i2i2i2−i2−i200000000000000000000000000000
χ6144-44-4-44-4-20000-22-22-2224-42i2−2i22i2−2i20000000000000002i2−2i2-2200−i2i2−i2i2−i2−i2i2i200000000000000000000000000000
χ6244-44-4-44-4-20000-22-22-222-44−2i22i2−2i22i20000000000000002i2−2i22-200i2−i2i2−i2−i2−i2i2i200000000000000000000000000000
χ6344-44-4-44-4-20000-22-22-222-442i2−2i22i2−2i2000000000000000−2i22i22-200−i2i2−i2i2i2i2−i2−i200000000000000000000000000000
χ6444-4-44-4-44400004-4-4-4-4440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ6544-4-44-4-44400004-4-4-4-44400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ6644-4-44-4-44-20000-22222-2-20022−22−22220000000000000000000−2i32i3−222−2i6−i6−i6i600000000000000000000000000000
χ6744-4-44-4-44-20000-22222-2-20022−22−222200000000000000000002i3−2i3−222−2−i6i6i6−i600000000000000000000000000000
χ6844-4-44-4-44-20000-22222-2-200−222222−220000000000000000000−2i32i32−2−22−i6i6i6−i600000000000000000000000000000
χ6944-4-44-4-44-20000-22222-2-200−222222−2200000000000000000002i3−2i32−2−22i6−i6−i6i600000000000000000000000000000
χ704-4444-4-4-4-24-4-4422-2-22-22000000-2-2220000000004i−4i000000000000000000000000000000000−2i2i00000000
χ714-4444-4-4-4-24-4-4422-2-22-22000000-2-222000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ724-4444-4-4-4-2-444-422-2-22-2200000022-2-20000004-40000000000000000000000000000000000-220000000000
χ734-4444-4-4-4-2-444-422-2-22-2200000022-2-2000000-4400000000000000000000000000000000002-20000000000
χ744-44-4-4-444444-4-4-4-4-444-44000000-444-4000000000000000000000000000000000000000000000000000000
χ754-44-4-4-444-244-4-4222-2-22-20000002-2-220000000000000000000000000000000000000000−2i32i3000000000000
χ764-44-4-4-444-244-4-4222-2-22-20000002-2-2200000000000000000000000000000000000000002i3−2i3000000000000
χ774-44-4-4-444-2-4-444222-2-22-2000000-222-200004-400000000000000000000000000000000-2200000000000000
χ784-44-4-4-444-2-4-444222-2-22-2000000-222-20000-44000000000000000000000000000000002-200000000000000
χ794-4-44-44-4440000-444-4-4-4400000000004-4-4400000000000000000000000000000000000000000000000000
χ804-4-44-44-4440000-444-4-4-440000000000-444-400000000000000000000000000000000000000000000000000
χ814-4-4-4444-440000-44-4-444-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ824-4-4-4444-440000-44-4-444-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ838-8-88-88-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

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