Finite Group Databasebeta

← Group #10844768

Character table — Group #10844768

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222222234444444466666664412121212121212124444444412121212121212121212121212121212121288888888246612122244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911111111111-1-1-1-1111111111-1-11111-1-1-1-1111-1-1-11-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-11111-1-11-1
χ1011111111111-1-1-1-1111111111-1-11111-1-1-1-1111-1-1-11-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-111-11
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-111-11-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-111-11
χ1211111111111-1-1-1-1111111111-1-11111-1-1-1-111-11-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-111-1-11-1
χ1311111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-11-1111-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1-1-11
χ1411111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-11-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-1111-1
χ1511111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1111-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-111-1-111-1-1-1-1111-1
χ1611111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-11111-1-1-11
χ17222222222-2-22222-2-22222222-2-2-2-2-2-22222002-200-2200000000-2-222-2-222-2-2000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2222200-22002-200000000-2-2-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2002200-2-2000000002222-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200-2-200220000000022-2-22222-2-2000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1111111110000000022-1-1-1-10000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111222-2-2-22-2-1-1-1-1111111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-1111122-22-2-2-22-1-1-1-11111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-22-2222-21111-1-1-1-111-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-2-2222-221111-1-1-1-1111111-1-1-1-1000000002-2-1-1110000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1002-200-22−i3−i3i3i3−i3−i3i3i311-1-111-1-1110000000000−i3i3−i3i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1002-200-22i3i3−i3−i3i3i3−i3−i311-1-111-1-1110000000000i3−i3i3−i30000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-100-22002-2−i3−i3i3i3−i3−i3i3i31111-1-111-1-10000000000i3−i3i3−i30000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-100-22002-2i3i3−i3−i3i3i3−i3−i31111-1-111-1-10000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111002200-2-2−i3−i3i3i3i3i3−i3−i3-1-1-1-11111-1-10000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111002200-2-2i3i3−i3−i3−i3−i3i3i3-1-1-1-11111-1-10000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100-2-20022−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-1110000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100-2-20022i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-1110000000000−i3i3i3−i30000000000
χ372222-2-2-2-222-20000-222-22-22-2-20022-2-2000000002i−2i0000002i−2i2i−2i00000000002i2i−2i−2i00000000002-200000000
χ382222-2-2-2-222-20000-222-22-22-2-20022-2-2000000002i−2i0000002i−2i2i−2i0000000000−2i−2i2i2i0000000000-2200000000
χ392222-2-2-2-222-20000-222-22-22-2-20022-2-200000000−2i2i000000−2i2i−2i2i00000000002i2i−2i−2i0000000000-2200000000
χ402222-2-2-2-222-20000-222-22-22-2-20022-2-200000000−2i2i000000−2i2i−2i2i0000000000−2i−2i2i2i00000000002-200000000
χ412-2-222-2-2222222-2-2-2-2-2-2-2-22222-22-22-222-2-200000000000000002-2000000002i−2i2i−2i2i2i−2i−2i0000000000000000
χ422-2-222-2-2222222-2-2-2-2-2-2-2-22222-22-22-222-2-200000000000000002-200000000−2i2i−2i2i−2i−2i2i2i0000000000000000
χ432-2-222-2-22222-2-222-2-2-2-2-2-2222-222-22-2-2-2220000000000000000-22000000002i−2i2i−2i−2i−2i2i2i0000000000000000
χ442-2-222-2-22222-2-222-2-2-2-2-2-2222-222-22-2-2-2220000000000000000-2200000000−2i2i−2i2i2i2i−2i−2i0000000000000000
χ452-2-222-2-222-2-222-2-222-2-2-2-2222-22-22-2222-2-20000000000000000-22000000000000000000000000002-22-200
χ462-2-222-2-222-2-222-2-222-2-2-2-2222-22-22-2222-2-20000000000000000-2200000000000000000000000000-22-2200
χ472-2-222-2-222-2-2-2-22222-2-2-2-22222-2-22-22-2-22200000000000000002-2000000000000000000000000002-2-2200
χ482-2-222-2-222-2-2-2-22222-2-2-2-22222-2-22-22-2-22200000000000000002-200000000000000000000000000-222-200
χ492-2-22-222-222-200002-2-22-222-2-2002-2-2200002i−2i0000002i−2i2i−2i000000000000002-2-220000000000002i−2i000000
χ502-2-22-222-222-200002-2-22-222-2-2002-2-2200002i−2i0000002i−2i2i−2i00000000000000-222-2000000000000−2i2i000000
χ512-2-22-222-222-200002-2-22-222-2-2002-2-220000−2i2i000000−2i2i−2i2i000000000000002-2-22000000000000−2i2i000000
χ522-2-22-222-222-200002-2-22-222-2-2002-2-220000−2i2i000000−2i2i−2i2i00000000000000-222-20000000000002i−2i000000
χ534444-4-4-4-44-4400004-44-44-44-4-400-4-444000000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-24-40000-44-22-22-22200-2-222000000004i−4i000000−2i2i−2i2i0000000000000000000000000000000000
χ554444-4-4-4-4-24-40000-44-22-22-22200-2-22200000000−4i4i0000002i−2i2i−2i0000000000000000000000000000000000
χ564444-4-4-4-4-2-4400004-4-22-22-2220022-2-2000000000000000023−23−23230000000000000000000000000000000000
χ574444-4-4-4-4-2-4400004-4-22-22-2220022-2-20000000000000000−232323−230000000000000000000000000000000000
χ5844-4-44-44-44004i−4i4i−4i004-4-44-44-40000004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-4-44-44-4400−4i4i−4i4i004-4-44-44-4000000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-2004i−4i4i−4i00-222-22-22000000−2i2i−2i2i0000000000000000000023−2300−2i32i3000000000000000000000000
χ6144-4-44-44-4-2004i−4i4i−4i00-222-22-22000000−2i2i−2i2i00000000000000000000−2323002i3−2i3000000000000000000000000
χ6244-4-44-44-4-200−4i4i−4i4i00-222-22-220000002i−2i2i−2i0000000000000000000023−23002i3−2i3000000000000000000000000
χ6344-4-44-44-4-200−4i4i−4i4i00-222-22-220000002i−2i2i−2i00000000000000000000−232300−2i32i3000000000000000000000000
χ6444-4-4-44-4440000000044-4-4-4-440000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ6544-4-4-44-4440000000044-4-4-4-4400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ664-44-444-4-44004i−4i−4i4i00-444-4-44-40000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ674-44-444-4-4400−4i4i4i−4i00-444-4-44-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ684-44-444-4-4-2004i−4i−4i4i002-2-222-22000000−2i2i2i−2i000000000000000000−2i32i30023−2300000000000000000000000000
χ694-44-444-4-4-2004i−4i−4i4i002-2-222-22000000−2i2i2i−2i0000000000000000002i3−2i300−232300000000000000000000000000
χ704-44-444-4-4-200−4i4i4i−4i002-2-222-220000002i−2i−2i2i000000000000000000−2i32i300−232300000000000000000000000000
χ714-44-444-4-4-200−4i4i4i−4i002-2-222-220000002i−2i−2i2i0000000000000000002i3−2i30023−2300000000000000000000000000
χ724-44-4-4-444400000000-4-444-4-44000000000000000000000000000000000000000022−22−22220000000000000000
χ734-44-4-4-444400000000-4-444-4-440000000000000000000000000000000000000000−222222−220000000000000000
χ744-4-444-4-44-24444-4-4-4-42222-2-2-24-4-22-22-2-2220000000000000000-2200000000000000000000000000000000
χ754-4-444-4-44-244-4-444-4-42222-2-2-2-44-22-2222-2-200000000000000002-200000000000000000000000000000000
χ764-4-444-4-44-2-4-444-4-4442222-2-2-2-442-22-2-2-22200000000000000002-200000000000000000000000000000000
χ774-4-444-4-44-2-4-4-4-444442222-2-2-24-42-22-222-2-20000000000000000-2200000000000000000000000000000000
χ784-4-44-444-44-440000-44-44-444-4-400-444-4000000000000000000000000000000000000000000000000000000
χ794-4-44-444-4-24-400004-42-22-2-22200-222-200004i−4i000000−2i2i−2i2i00000000000000000000000000000000000000
χ804-4-44-444-4-24-400004-42-22-2-22200-222-20000−4i4i0000002i−2i2i−2i00000000000000000000000000000000000000
χ814-4-44-444-4-2-440000-442-22-2-222002-2-2200000000000023−23−232300000000000000000000000000000000000000
χ824-4-44-444-4-2-440000-442-22-2-222002-2-22000000000000−232323−2300000000000000000000000000000000000000
χ8388-8-8-88-88-400000000-4-44444-4000000000000000000000000000000000000000000000000000000000000
χ848-88-8-8-888-40000000044-4-444-4000000000000000000000000000000000000000000000000000000000000

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