Finite Group Databasebeta

← Group #10855272

Character table — Group #10855272

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424244444444488884121212121212121222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1
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
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1-1111-1-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-11111-1-11-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-111-111-1
χ911111111111111111111-1-1111111111111-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111111-111-1-1-1-11111-1-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-11111-1-1-1-111-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-11111-1-111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-111111111-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111-1-1-1-111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-11111-1-1-1-11-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-22222-20000000022-2-200000000-2-222000000000000000000000-2000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-20000000022-2-20000000000000000000002000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222200000000-2-22200000000-2-2-2-20000000000000000000002000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000-2-222000000002222000000000000000000000-2000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-2-2-1-1-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-2-2-222-2-2-1-1-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-222-2-222-2-21111-1-1-1-11111000000000000-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-222-2-2-2-21111-1-1-1-11111000000000000211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-222-2-2-2-22211111111-1-1-1-10000000000002-1-1-1-1111100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222222211111111-1-1-1-1000000000000-21111-1-1-1-100000000
χ2922-22-2-22-22-22-2222-2-2-22-2000000-2-2220000000002i−2i00000000000000000022-2-22i2i−2i−2i00000002i−2i00000000
χ3022-22-2-22-22-22-2222-2-2-22-2000000-2-2220000000002i−2i000000000000000000-2-222−2i−2i2i2i00000002i−2i00000000
χ3122-22-2-22-22-22-2222-2-2-22-2000000-2-222000000000−2i2i00000000000000000022-2-2−2i−2i2i2i0000000−2i2i00000000
χ3222-22-2-22-22-22-2222-2-2-22-2000000-2-222000000000−2i2i000000000000000000-2-2222i2i−2i−2i0000000−2i2i00000000
χ3322-2-22-2-22200002-22-2-2-222i−2i−i2−i2i2i2000022-2-200000002−22i−2i00−i2−i2i2i222−2−2002i−2i0000−i2i2−i2i2000000000000002−20
χ3422-2-22-2-22200002-22-2-2-222i−2i−i2−i2i2i20000-2-22200000002−22i−2i00−i2−i2i2i222−2−200−2i2i0000i2−i2i2−i200000000000000−220
χ3522-2-22-2-22200002-22-2-2-222i−2ii2i2−i2−i2000022-2-20000000−222i−2i00i2i2−i2−i2−2−222002i−2i0000i2−i2i2−i200000000000000−220
χ3622-2-22-2-22200002-22-2-2-222i−2ii2i2−i2−i20000-2-2220000000−222i−2i00i2i2−i2−i2−2−22200−2i2i0000−i2i2−i2i2000000000000002−20
χ3722-2-22-2-22200002-22-2-2-22−2i2i−i2−i2i2i2000022-2-20000000−22−2i2i00−i2−i2i2i2−2−22200−2i2i0000−i2i2−i2i200000000000000−220
χ3822-2-22-2-22200002-22-2-2-22−2i2i−i2−i2i2i20000-2-2220000000−22−2i2i00−i2−i2i2i2−2−222002i−2i0000i2−i2i2−i2000000000000002−20
χ3922-2-22-2-22200002-22-2-2-22−2i2ii2i2−i2−i2000022-2-200000002−2−2i2i00i2i2−i2−i222−2−200−2i2i0000i2−i2i2−i2000000000000002−20
χ4022-2-22-2-22200002-22-2-2-22−2i2ii2i2−i2−i20000-2-22200000002−2−2i2i00i2i2−i2−i222−2−2002i−2i0000−i2i2−i2i200000000000000−220
χ412-22-22-22-222-2-22-2-222-22-20000002-22-22i−2i2i−2i02i−2i0000000000000000002i−2i002-22-2000002i−2i00000000000000
χ422-22-22-22-222-2-22-2-222-22-20000002-22-22i−2i2i−2i0−2i2i0000000000000000002i−2i00-22-2200000−2i2i00000000000000
χ432-22-22-22-222-2-22-2-222-22-20000002-22-2−2i2i−2i2i02i−2i000000000000000000−2i2i00-22-22000002i−2i00000000000000
χ442-22-22-22-222-2-22-2-222-22-20000002-22-2−2i2i−2i2i0−2i2i000000000000000000−2i2i002-22-200000−2i2i00000000000000
χ452-22-22-22-22-222-2-2-222-22-2000000-22-222i−2i2i−2i0002i−2i0000000000000000−2i2i0000000000000002i−2i00002-20000
χ462-22-22-22-22-222-2-2-222-22-2000000-22-222i−2i2i−2i000−2i2i0000000000000000−2i2i000000000000000−2i2i0000-220000
χ472-22-22-22-22-222-2-2-222-22-2000000-22-22−2i2i−2i2i0002i−2i00000000000000002i−2i0000000000000002i−2i0000-220000
χ482-22-22-22-22-222-2-2-222-22-2000000-22-22−2i2i−2i2i000−2i2i00000000000000002i−2i000000000000000−2i2i00002-20000
χ492-2-2-2-22222-2-222-2-2-2-2222002-22-2-222-2000000000000000002-22-2000000002-2-2200000000000002-2000000
χ502-2-2-2-22222-2-222-2-2-2-2222002-22-2-222-2000000000000000002-22-200000000-222-20000000000000-22000000
χ512-2-2-2-22222-2-222-2-2-2-222200-22-22-222-200000000000000000-22-22000000002-2-220000000000000-22000000
χ522-2-2-2-22222-2-222-2-2-2-222200-22-22-222-200000000000000000-22-2200000000-222-200000000000002-2000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000-400000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000040000000022-2-20000000000000000000000000000000000000
χ55444-4-44-4-4400004-4-444-4-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ56444-4-44-4-4400004-4-444-4-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ5744-44-4-44-444-44-444-4-4-44-400000044-4-4000000000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-24-44-4-2-2222-22000000-2-2220000000000000000000000000000000000000000−2i32i3000000000000
χ5944-44-4-44-4-24-44-4-2-2222-22000000-2-22200000000000000000000000000000000000000002i3−2i3000000000000
χ6044-44-4-44-4-2-44-44-2-2222-2200000022-2-20000000004i−4i000000000000000000000000000000000−2i2i00000000
χ6144-44-4-44-4-2-44-44-2-2222-2200000022-2-2000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ6244-4-44-4-44-20000-22-2222-24i−4i−2i2−2i22i22i200000000000000022−22−2i2i00i2i2−i2−i2−2−22200000000000000000000000000000
χ6344-4-44-4-44-20000-22-2222-24i−4i2i22i2−2i2−2i2000000000000000−2222−2i2i00−i2−i2i2i222−2−200000000000000000000000000000
χ6444-4-44-4-44-20000-22-2222-2−4i4i−2i2−2i22i22i2000000000000000−22222i−2i00i2i2−i2−i222−2−200000000000000000000000000000
χ6544-4-44-4-44-20000-22-2222-2−4i4i2i22i2−2i2−2i200000000000000022−222i−2i00−i2−i2i2i2−2−22200000000000000000000000000000
χ664-444-4-4-4440000-44-44-4-4400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ674-444-4-4-4440000-44-44-4-44002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ684-444-4-4-44-200002-22-222-200−2i22i22i2−2i2000000000000000000023−23i2−i2−i2i2i6−i6i6−i600000000000000000000000000000
χ694-444-4-4-44-200002-22-222-200−2i22i22i2−2i20000000000000000000−2323i2−i2−i2i2−i6i6−i6i600000000000000000000000000000
χ704-444-4-4-44-200002-22-222-2002i2−2i2−2i22i2000000000000000000023−23−i2i2i2−i2−i6i6−i6i600000000000000000000000000000
χ714-444-4-4-44-200002-22-222-2002i2−2i2−2i22i20000000000000000000−2323−i2i2i2−i2i6−i6i6−i600000000000000000000000000000
χ724-44-44-44-4-24-4-4422-2-22-22000000-22-22000004i−4i0000000000000000000000000000000−2i2i00000000000000
χ734-44-44-44-4-24-4-4422-2-22-22000000-22-2200000−4i4i00000000000000000000000000000002i−2i00000000000000
χ744-44-44-44-4-2-444-422-2-22-220000002-22-200000004i−4i000000000000000000000000000000000−2i2i0000000000
χ754-44-44-44-4-2-444-422-2-22-220000002-22-20000000−4i4i0000000000000000000000000000000002i−2i0000000000
χ764-4-4444-4-440000-444-44-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ774-4-4444-4-440000-444-44-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ784-4-4-4-4444444-4-4-4-4-4-44440000004-4-44000000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-244-4-42222-2-2-2000000-222-2000000000000000000000−2i32i32i3−2i300000000000000000000000000000
χ804-4-4-4-4444-244-4-42222-2-2-2000000-222-20000000000000000000002i3−2i3−2i32i300000000000000000000000000000
χ814-4-4-4-4444-2-4-4442222-2-2-2004-44-42-2-2200000000000000000-22-22000000000000000000000000000000000
χ824-4-4-4-4444-2-4-4442222-2-2-200-44-442-2-22000000000000000002-22-2000000000000000000000000000000000
χ83888-8-88-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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