Finite Group Databasebeta

← Group #10827355

Character table — Group #10827355

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666662288881212121244442222444668812122424242424242424224444448888466661212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111111111-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-11-1-111-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-111-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-111-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-1-11111-1
χ911111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-111-1-11
χ1011111111111111111111-1-1111111111111-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-11111-1-1-111-1-1-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-111111-1-111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111111
χ1311111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-1-1-11111-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-11111111111-11111-1-1-1-11-1-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1111111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222000000-22200-2-200000000-2-22200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000-22200-2-20000000022-2-20000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-222220000002-2-2002200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20000002-2-2002200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-2-2-22-1-122-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022-2-2222-1-1-2-2-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222-2-22-1-1-2-2-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-2-2-211-2-211-1-1-1-111110000000000002-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-22222-211-2-211-1-1-1-11111000000000000-211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-100002222-2-2-21122111111-1-1-1-1000000000000-2-1-1-1-1111100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-2-222-21122111111-1-1-1-100000000000021111-1-1-1-100000000
χ2922-222-2-2-2200002-2-2-222-22-222−2−200002i2i−2i−2i00000002-22−20022−2−222−2−2002i−2i0000−i2−i2i2i200000000000000−i2i20
χ3022-222-2-2-2200002-2-2-222-22-222−2−20000−2i−2i2i2i00000002-22−20022−2−222−2−200−2i2i0000i2i2−i2−i200000000000000i2−i20
χ3122-222-2-2-2200002-2-2-222-22-2−2−22200002i2i−2i−2i00000002-2−2200−2−222−2−222002i−2i0000i2i2−i2−i200000000000000i2−i20
χ3222-222-2-2-2200002-2-2-222-22-2−2−2220000−2i−2i2i2i00000002-2−2200−2−222−2−22200−2i2i0000−i2−i2i2i200000000000000−i2i20
χ3322-222-2-2-2200002-2-2-222-2-2222−2−200002i2i−2i−2i0000000-22−220022−2−2−2−22200−2i2i0000−i2−i2i2i200000000000000i2−i20
χ3422-222-2-2-2200002-2-2-222-2-2222−2−20000−2i−2i2i2i0000000-22−220022−2−2−2−222002i−2i0000i2i2−i2−i200000000000000−i2i20
χ3522-222-2-2-2200002-2-2-222-2-22−2−22200002i2i−2i−2i0000000-222−200−2−22222−2−200−2i2i0000i2i2−i2−i200000000000000−i2i20
χ3622-222-2-2-2200002-2-2-222-2-22−2−2220000−2i−2i2i2i0000000-222−200−2−22222−2−2002i−2i0000−i2−i2i2i200000000000000i2−i20
χ3722-2-2-222-222-22-222-2-2-2-22002i−2i2i−2i22-2-2000000000000000002i−2i2i−2i000000002i2i−2i−2i000000000000002-200000
χ3822-2-2-222-222-22-222-2-2-2-22002i−2i2i−2i22-2-2000000000000000002i−2i2i−2i00000000−2i−2i2i2i00000000000000-2200000
χ3922-2-2-222-222-22-222-2-2-2-2200−2i2i−2i2i22-2-200000000000000000−2i2i−2i2i000000002i2i−2i−2i00000000000000-2200000
χ4022-2-2-222-222-22-222-2-2-2-2200−2i2i−2i2i22-2-200000000000000000−2i2i−2i2i00000000−2i−2i2i2i000000000000002-200000
χ412-222-2-22-2222-2-2-2-22-22-220000002-22-20000002-20000000000000000000002i−2i2i−2i2i−2i2i−2i0002-2000000000000
χ422-222-2-22-2222-2-2-2-22-22-220000002-22-20000002-2000000000000000000000−2i2i−2i2i−2i2i−2i2i0002-2000000000000
χ432-222-2-22-2222-2-2-2-22-22-220000002-22-2000000-220000000000000000000002i−2i2i−2i−2i2i−2i2i000-22000000000000
χ442-222-2-22-2222-2-2-2-22-22-220000002-22-2000000-22000000000000000000000−2i2i−2i2i2i−2i2i−2i000-22000000000000
χ452-2-2-22-22222-2-22-2-2-22-2220000002-2-222-22-200002-20000000000000002-2002-2-220000000002-20000000000
χ462-2-2-22-22222-2-22-2-2-22-2220000002-2-222-22-20000-220000000000000002-200-222-2000000000-220000000000
χ472-2-2-22-22222-2-22-2-2-22-2220000002-2-22-22-2200002-2000000000000000-2200-222-20000000002-20000000000
χ482-2-2-22-22222-2-22-2-2-22-2220000002-2-22-22-220000-22000000000000000-22002-2-22000000000-220000000000
χ492-2-2-22-2222-222-2-2-2-22-222000000-222-22-22-22-20000000000000000000-22000000000002-20000000002-2000
χ502-2-2-22-2222-222-2-2-2-22-222000000-222-22-22-2-220000000000000000000-2200000000000-22000000000-22000
χ512-2-2-22-2222-222-2-2-2-22-222000000-222-2-22-222-200000000000000000002-2000000000002-2000000000-22000
χ522-2-2-22-2222-222-2-2-2-22-222000000-222-2-22-22-2200000000000000000002-200000000000-220000000002-2000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000000000-4-2-200220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000000042200-2-20000000000000000000000000000000000000
χ55444-4-4-4-44400004-444-4-4-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ56444-4-4-4-44400004-444-4-4-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ57444-4-4-4-44-20000-22-2-222200−2i22i22i2−2i2000000000000000000023−23i2−i2−i2i2i6−i6i6−i600000000000000000000000000000
χ58444-4-4-4-44-20000-22-2-222200−2i22i22i2−2i20000000000000000000−2323i2−i2−i2i2−i6i6−i6i600000000000000000000000000000
χ59444-4-4-4-44-20000-22-2-2222002i2−2i2−2i22i2000000000000000000023−23−i2i2i2−i2−i6i6−i6i600000000000000000000000000000
χ60444-4-4-4-44-20000-22-2-2222002i2−2i2−2i22i20000000000000000000−2323−i2i2i2−i2i6−i6i6−i600000000000000000000000000000
χ6144-444-4-4-4-20000-2222-2-224-42222−22−22000000000000000-2222−2200−2−222−2−22200000000000000000000000000000
χ6244-444-4-4-4-20000-2222-2-224-4−22−222222000000000000000-22−22220022−2−222−2−200000000000000000000000000000
χ6344-444-4-4-4-20000-2222-2-22-442222−22−220000000000000002-2−222200−2−22222−2−200000000000000000000000000000
χ6444-444-4-4-4-20000-2222-2-22-44−22−2222220000000000000002-222−220022−2−2−2−22200000000000000000000000000000
χ6544-4-4-444-44-44-4444-4-4-4-44000000-4-444000000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4-24-44-4-2-22222-2004i−4i4i−4i-2-22200000000000000000−2i2i−2i2i000000000000000000000000000000000
χ6744-4-4-444-4-24-44-4-2-22222-200−4i4i−4i4i-2-222000000000000000002i−2i2i−2i000000000000000000000000000000000
χ6844-4-4-444-4-2-44-44-2-22222-200000022-2-2000000000000000000000−2i32i32i3−2i300000000000000000000000000000
χ6944-4-4-444-4-2-44-44-2-22222-200000022-2-20000000000000000000002i3−2i3−2i32i300000000000000000000000000000
χ704-444-4-44-44-4-444-4-44-44-44000000-44-44000000000000000000000000000000000000000000000000000000
χ714-444-4-44-4-244-4-422-22-22-2000000-22-220000004-400000000000000000000000000000000-22000000000000
χ724-444-4-44-4-244-4-422-22-22-2000000-22-22000000-44000000000000000000000000000000002-2000000000000
χ734-444-4-44-4-2-4-44422-22-22-20000002-22-200000000000000000000000000000000000000000000−2i32i300000000
χ744-444-4-44-4-2-4-44422-22-22-20000002-22-2000000000000000000000000000000000000000000002i3−2i300000000
χ754-44-444-4-440000-444-4-44-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ764-44-444-4-440000-444-4-44-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ774-4-44-44-4440000-44-444-4-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ784-4-44-44-4440000-44-444-4-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ794-4-4-44-444-24-4-44222-22-2-2000000-222-2000000004-400000000000000000000000000000000-220000000000
χ804-4-4-44-444-24-4-44222-22-2-2000000-222-200000000-44000000000000000000000000000000002-20000000000
χ814-4-4-44-444-2-444-4222-22-2-20000002-2-2200004-400000000000000000000000000000000-2200000000000000
χ824-4-4-44-444-2-444-4222-22-2-20000002-2-220000-44000000000000000000000000000000002-200000000000000
χ838-88-888-8-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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