Finite Group Databasebeta

← Group #10697516

Character table — Group #10697516

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222444444666612121212121212121212121212128888888844121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-22-22222222-2-22222-2-2-2-22200-2-2002222-2-20000-2-2-2-20000000000000000000000000000
χ10222222222222-2-2-22-22222222-2-22222-2-2-2-2-2-2002200-2-2-2-2-2-2000022220000000000000000000000000000
χ11222222222-2-2-2222-222222222-2-2-2-2-2-22222002200-2-20000-2-222220000-2-2-2-2000000000000000000000000
χ12222222222-2-2-2222-222222222-2-2-2-2-2-2222200-2-200220000-2-2-2-2-2-200002222000000000000000000000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000000002-222-2-20000000000
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000-22-2-2220000000000
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-1111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-1-11111-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111111111110000000022-1-1-1-10000000000
χ1922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-1-111112200-2-200-1-1-1-111−i3−i3i3i31111−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-1-111112200-2-200-1-1-1-111i3i3−i3−i31111i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2122222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-2002200111111−i3−i3i3i3-1-1-1-1−i3−i3i3i30000000000i3−i3i3−i30000000000
χ2222222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-2002200111111i3i3−i3−i3-1-1-1-1i3i3−i3−i30000000000−i3i3−i3i30000000000
χ2322222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-21111-1-1-1-1002200-2-2−i3−i3i3i311-1-1-1-1−i3−i3i3i311110000000000−i3i3i3−i30000000000
χ2422222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-21111-1-1-1-1002200-2-2i3i3−i3−i311-1-1-1-1i3i3−i3−i311110000000000i3−i3−i3i30000000000
χ2522222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-21111-1-1-1-100-2-20022−i3−i3i3i3111111−i3−i3i3i3-1-1-1-10000000000i3−i3−i3i30000000000
χ2622222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-21111-1-1-1-100-2-20022i3i3−i3−i3111111i3i3−i3−i3-1-1-1-10000000000−i3i3i3−i30000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000002-2-1-1110000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000-2211-1-10000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000-2211-1-10000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000002-2-1-1110000000000
χ31222-22-2-2-2222-2000-2022-22-2-2-20022-2-200002-20000002-22-2000000000000002222−2−2−2−200000022−2−2000000
χ32222-22-2-2-2222-2000-2022-22-2-2-20022-2-200002-20000002-22-200000000000000−2−2−2−22222000000−2−222000000
χ33222-22-2-2-2222-2000-2022-22-2-2-20022-2-20000-22000000-22-22000000000000002222−2−2−2−2000000−2−222000000
χ34222-22-2-2-2222-2000-2022-22-2-2-20022-2-20000-22000000-22-2200000000000000−2−2−2−2222200000022−2−2000000
χ3522-22-2-2-22200022-20-22-22-2-2-2200000022-2-2002i−2i00000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000022−2−200
χ3622-22-2-2-22200022-20-22-22-2-2-2200000022-2-2002i−2i00000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000−2−22200
χ3722-22-2-2-22200022-20-22-22-2-2-2200000022-2-200−2i2i0000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000−2−22200
χ3822-22-2-2-22200022-20-22-22-2-2-2200000022-2-200−2i2i0000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000022−2−200
χ392-22-2-2-22220002-2-202-22-2-2-2220000002-22-20000002-2000000000000002-22-22−22−22−22−200000000002−22−200
χ402-22-2-2-22220002-2-202-22-2-2-2220000002-22-20000002-2000000000000002-22-2−22−22−22−220000000000−22−2200
χ412-22-2-2-22220002-2-202-22-2-2-2220000002-22-2000000-2200000000000000-22-222−22−22−22−20000000000−22−2200
χ422-22-2-2-22220002-2-202-22-2-2-2220000002-22-2000000-2200000000000000-22-22−22−22−22−2200000000002−22−200
χ432-2-222-22-222-2-200020-2-222-22-2002-22-2000000002i−2i0000000000002i−2i2i−2i0000−i2i2i2−i2i2−i2−i2i20000002−22−2000000
χ442-2-222-22-222-2-200020-2-222-22-2002-22-2000000002i−2i0000000000002i−2i2i−2i0000i2−i2−i2i2−i2i2i2−i2000000−22−22000000
χ452-2-222-22-222-2-200020-2-222-22-2002-22-200000000−2i2i000000000000−2i2i−2i2i0000−i2i2i2−i2i2−i2−i2i2000000−22−22000000
χ462-2-222-22-222-2-200020-2-222-22-2002-22-200000000−2i2i000000000000−2i2i−2i2i0000i2−i2−i2i2−i2i2i2−i20000002−22−2000000
χ472-2-2-222-2222-222-22-2-2-2-2-222-222-22-2-222-2-220000000000002-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ482-2-2-222-2222-222-22-2-2-2-2-222-222-22-2-222-2-220000000000002-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ492-2-2-222-2222-22-22-2-22-2-2-222-22-222-2-22-222-2000000000000-22000000000000000000000000002-2-22000000
χ502-2-2-222-2222-22-22-2-22-2-2-222-22-222-2-22-222-2000000000000-2200000000000000000000000000-222-2000000
χ512-2-2-222-222-22-22-222-2-2-2-222-22-22-222-22-2-22000000000000-220000000000000000000000000000002-2-2200
χ522-2-2-222-222-22-22-222-2-2-2-222-22-22-222-22-2-22000000000000-22000000000000000000000000000000-222-200
χ532-2-2-222-222-22-2-22-222-2-2-222-222-2-222-2-222-20000000000002-200000000000000000000000000000000002-2
χ542-2-2-222-222-22-2-22-222-2-2-222-222-2-222-2-222-20000000000002-20000000000000000000000000000000000-22
χ55444-44-4-4-44-4-440004044-44-4-4-400-4-444000000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-244-4000-40-2-22-222200-2-22200004-4000000-22-2200000000000000000000000000000000000000
χ57444-44-4-4-4-244-4000-40-2-22-222200-2-2220000-440000002-22-200000000000000000000000000000000000000
χ58444-44-4-4-4-2-4-4400040-2-22-22220022-2-2000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ59444-44-4-4-4-2-4-4400040-2-22-22220022-2-20000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ6044-44-4-4-444000-4-44044-44-4-4-44000000-4-44400000000000000000000000000000000000000000000000000
χ6144-44-4-4-44-200044-40-4-22-2222-2000000-2-222004i−4i0000000000−2i2i−2i2i00000000000000000000000000000000
χ6244-44-4-4-44-200044-40-4-22-2222-2000000-2-22200−4i4i00000000002i−2i2i−2i00000000000000000000000000000000
χ6344-44-4-4-44-2000-4-4404-22-2222-200000022-2-20000000000000023−23−232300000000000000000000000000000000
χ6444-44-4-4-44-2000-4-4404-22-2222-200000022-2-200000000000000−232323−2300000000000000000000000000000000
χ6544-4-4-444-44000000004-4-4-444-40000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ6644-4-4-444-44000000004-4-4-444-4000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ674-444-44-4-4400000000-444-44-4-40000000000000000000000000000000000002-22-2-22-220000000000000000
χ684-444-44-4-4400000000-444-44-4-4000000000000000000000000000000000000-22-222-22-20000000000000000
χ694-44-4-4-4444000-4440-4-44-4-4-444000000-44-4400000000000000000000000000000000000000000000000000
χ704-44-4-4-444-20004-4-4042-2222-2-2000000-22-220000004-400000000000000-22-22000000000000000000000000
χ714-44-4-4-444-20004-4-4042-2222-2-2000000-22-22000000-44000000000000002-22-2000000000000000000000000
χ724-44-4-4-444-2000-4440-42-2222-2-20000002-22-20000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ734-44-4-4-444-2000-4440-42-2222-2-20000002-22-200000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ744-4-444-44-44-444000-40-4-444-44-400-44-44000000000000000000000000000000000000000000000000000000
χ754-4-444-44-4-24-4-40004022-2-22-2200-22-22000000004i−4i000000000000−2i2i−2i2i0000000000000000000000000000
χ764-4-444-44-4-24-4-40004022-2-22-2200-22-2200000000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000
χ774-4-444-44-4-2-444000-4022-2-22-22002-22-2000000000000000000000023−23−23230000000000000000000000000000
χ784-4-444-44-4-2-444000-4022-2-22-22002-22-20000000000000000000000−232323−230000000000000000000000000000
χ794-4-4-444-44-24-444-44-4-4222-2-22-24-4-222-2-222-2000000000000-22000000000000000000000000000000000000
χ804-4-4-444-44-24-44-44-4-44222-2-22-2-44-222-22-2-220000000000002-2000000000000000000000000000000000000
χ814-4-4-444-44-2-44-44-444-4222-2-22-2-442-2-22-222-20000000000002-2000000000000000000000000000000000000
χ824-4-4-444-44-2-44-4-44-444222-2-22-24-42-2-222-2-22000000000000-22000000000000000000000000000000000000
χ8388-8-8-888-8-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-4000000004-4-44-444000000000000000000000000000000000000000000000000000000000000

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