Finite Group Databasebeta

← Group #10867937

Character table — Group #10867937

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424242244444488884121212121212121244444884
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
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1111-1-111-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-111-1-1111
χ911111111111111111111-1-1111111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-11111-1-1-1-1-111-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-111-1-11
χ1111111111111111111111-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-111-1
χ1311111111111111111111-1-1-1-1-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1111111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111111-111-1-1-1-1111-1-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222-20000000022-2-20000000022-2-200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-200000000-2-2220000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222200000000-2-22200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000-2-22200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-2-2-2-2-2-1-1-1-1111111110000000000002-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-22222-2-2-1-1-1-111111111000000000000-211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-22222-2-2-2-21111-1-1-1-11111000000000000-2-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-2-222-2-21111-1-1-1-1111100000000000021111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-222-2-2222211111111-1-1-1-1000000000000-2-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222-2-22211111111-1-1-1-1000000000000211-1-1-1-11100000000
χ292222-2-2-2-22000022-22-2-2-22-222−2−2000022-2-200000002−22-20022−2−222−2−22-200000022−2−2000000000000002−20
χ302222-2-2-2-22000022-22-2-2-22-222−2−20000-2-22200000002−22-20022−2−222−2−2-22000000−2−22200000000000000−220
χ312222-2-2-2-22000022-22-2-2-22-2−2−222000022-2-20000000−222-200−2−222−2−2222-2000000−2−22200000000000000−220
χ322222-2-2-2-22000022-22-2-2-22-2−2−2220000-2-2220000000−222-200−2−222−2−222-2200000022−2−2000000000000002−20
χ332222-2-2-2-22000022-22-2-2-2-2222−2−2000022-2-20000000−22-220022−2−2−2−222-2200000022−2−200000000000000−220
χ342222-2-2-2-22000022-22-2-2-2-2222−2−20000-2-2220000000−22-220022−2−2−2−2222-2000000−2−222000000000000002−20
χ352222-2-2-2-22000022-22-2-2-2-22−2−222000022-2-200000002−2-2200−2−22222−2−2-22000000−2−222000000000000002−20
χ362222-2-2-2-22000022-22-2-2-2-22−2−2220000-2-22200000002−2-2200−2−22222−2−22-200000022−2−200000000000000−220
χ3722-2-2-22-22222-2-22-22-22-2-20000002-2-222i−2i2i−2i000002i−2i00000000000000002i−2i0000000000000002i−2i0002-2000
χ3822-2-2-22-22222-2-22-22-22-2-20000002-2-222i−2i2i−2i00000−2i2i00000000000000002i−2i000000000000000−2i2i000-22000
χ3922-2-2-22-22222-2-22-22-22-2-20000002-2-22−2i2i−2i2i000002i−2i0000000000000000−2i2i0000000000000002i−2i000-22000
χ4022-2-2-22-22222-2-22-22-22-2-20000002-2-22−2i2i−2i2i00000−2i2i0000000000000000−2i2i000000000000000−2i2i0002-2000
χ4122-2-2-22-222-2-2222-22-22-2-2000000-222-22i−2i2i−2i0002-2000000000000000000−2i2i2i2i−2i−2i00000002-2000000000000
χ4222-2-2-22-222-2-2222-22-22-2-2000000-222-22i−2i2i−2i000-22000000000000000000−2i2i−2i−2i2i2i0000000-22000000000000
χ4322-2-2-22-222-2-2222-22-22-2-2000000-222-2−2i2i−2i2i0002-20000000000000000002i−2i−2i−2i2i2i00000002-2000000000000
χ4422-2-2-22-222-2-2222-22-22-2-2000000-222-2−2i2i−2i2i000-220000000000000000002i−2i2i2i−2i−2i0000000-22000000000000
χ452-22-222-2-22-222-2-2-2-2222-2002-22-2-22-22000000000000000002-22-2000000002i−2i2i−2i000000000000002i−2i00000
χ462-22-222-2-22-222-2-2-2-2222-2002-22-2-22-22000000000000000002-22-200000000−2i2i−2i2i00000000000000−2i2i00000
χ472-22-222-2-22-222-2-2-2-2222-200-22-22-22-2200000000000000000-22-22000000002i−2i2i−2i00000000000000−2i2i00000
χ482-22-222-2-22-222-2-2-2-2222-200-22-22-22-2200000000000000000-22-2200000000−2i2i−2i2i000000000000002i−2i00000
χ492-2-22-222-222-22-2-22-2-22-2200000022-2-2000002i−2i00000000000000000000002-2-222i−2i2i−2i02i−2i00000000000000
χ502-2-22-222-222-22-2-22-2-22-2200000022-2-2000002i−2i0000000000000000000000-222-2−2i2i−2i2i02i−2i00000000000000
χ512-2-22-222-222-22-2-22-2-22-2200000022-2-200000−2i2i00000000000000000000002-2-22−2i2i−2i2i0−2i2i00000000000000
χ522-2-22-222-222-22-2-22-2-22-2200000022-2-200000−2i2i0000000000000000000000-222-22i−2i2i−2i0−2i2i00000000000000
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
χ554444-4-4-4-4-20000-2-22-22224-42222−22−2200000000000000022−22-2200−2−222−2−22200000000000000000000000000000
χ564444-4-4-4-4-20000-2-22-22224-4−22−222222000000000000000−2222-220022−2−222−2−200000000000000000000000000000
χ574444-4-4-4-4-20000-2-22-2222-442222−22−22000000000000000−22222-200−2−22222−2−200000000000000000000000000000
χ584444-4-4-4-4-20000-2-22-2222-44−22−22222200000000000000022−222-20022−2−2−2−22200000000000000000000000000000
χ5944-4-44-44-4400004-4-4-4-44400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-44-44-4400004-4-4-4-4440000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6144-4-4-44-44-244-4-4-22-22-222000000-222-20000000004i−4i000000000000000000000000000000000−2i2i00000000
χ6244-4-4-44-44-244-4-4-22-22-222000000-222-2000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ6344-4-4-44-44-2-4-444-22-22-2220000002-2-2200000004-40000000000000000000000000000000-22000000000000
χ6444-4-4-44-44-2-4-444-22-22-2220000002-2-220000000-4400000000000000000000000000000002-2000000000000
χ654-44-444-4-444-4-44-4-4-4444-40000004-44-4000000000000000000000000000000000000000000000000000000
χ664-44-444-4-4-24-4-44222-2-2-22000000-22-2200000000000000000000023−2323−2300000000000000000000000000000
χ674-44-444-4-4-24-4-44222-2-2-22000000-22-22000000000000000000000−2323−232300000000000000000000000000000
χ684-44-444-4-4-2-444-4222-2-2-22004-44-42-22-200000000000000000-22-22000000000000000000000000000000000
χ694-44-444-4-4-2-444-4222-2-2-2200-44-442-22-2000000000000000002-22-2000000000000000000000000000000000
χ704-44-4-4-44440000-4-444-4-440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ714-44-4-4-44440000-4-444-4-4400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ724-44-4-4-444-2000022-2-222-20022−22−2222000000000000000000023−23−222−26−6−6600000000000000000000000000000
χ734-44-4-4-444-2000022-2-222-20022−22−22220000000000000000000−2323−222−2−666−600000000000000000000000000000
χ744-44-4-4-444-2000022-2-222-200−222222−22000000000000000000023−232−2−22−666−600000000000000000000000000000
χ754-44-4-4-444-2000022-2-222-200−222222−220000000000000000000−23232−2−226−6−6600000000000000000000000000000
χ764-4-444-4-4440000-444-4-44-40000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ774-4-444-4-4440000-444-4-44-400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ784-4-44-444-44-44-44-44-4-44-44000000-4-444000000000000000000000000000000000000000000000000000000
χ794-4-44-444-4-24-44-42-222-22-2000000-2-222000004i−4i0000000000000000000000000000000−2i2i00000000000000
χ804-4-44-444-4-24-44-42-222-22-2000000-2-22200000−4i4i00000000000000000000000000000002i−2i00000000000000
χ814-4-44-444-4-2-44-442-222-22-200000022-2-2000000000000000000000000000000000000000000−2i32i30000000000
χ824-4-44-444-4-2-44-442-222-22-200000022-2-20000000000000000000000000000000000000000002i3−2i30000000000
χ8388-8-88-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000

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