Finite Group Databasebeta

← Group #10690958

Character table — Group #10690958

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222222222344446666666222244444466666666666612121212121212121212121212121212444412121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-222222222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2722222222-2-2-2-222222222222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ3722-2-222-2-22-22-2200002-2-222-2-20000002i−2i2i−2i22-2-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000002−22−2−i2i2−i2i2
χ3822-2-222-2-22-22-2200002-2-222-2-20000002i−2i2i−2i22-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−22−22i2−i2i2−i2
χ3922-2-222-2-22-22-2200002-2-222-2-2000000−2i2i−2i2i22-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000002−22−2i2−i2i2−i2
χ4022-2-222-2-22-22-2200002-2-222-2-2000000−2i2i−2i2i22-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000−22−22−i2i2−i2i2
χ4122-2-222-2-2-22-22200002-2-222-2-20000002i−2i−2i2i-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000−i2i2i2−i2−222−2
χ4222-2-222-2-2-22-22200002-2-222-2-20000002i−2i−2i2i-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000i2−i2−i2i22−2−22
χ4322-2-222-2-2-22-22200002-2-222-2-2000000−2i2i2i−2i-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000−i2i2i2−i22−2−22
χ4422-2-222-2-2-22-22200002-2-222-2-2000000−2i2i2i−2i-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000i2−i2−i2i2−222−2
χ4522-2-2-2-22222-2-2222-2-22-2-2-2-22200002-200002-22-20000000022-2-222-2-20000000000000000000000002i−2i2i−2i00000000
χ4622-2-2-2-22222-2-2222-2-22-2-2-2-22200002-200002-22-20000000022-2-222-2-2000000000000000000000000−2i2i−2i2i00000000
χ4722-2-2-2-22222-2-22-2-2222-2-2-2-2220000-2200002-22-200000000-2-222-2-222000000000000000000002i−2i2i−2i000000000000
χ4822-2-2-2-22222-2-22-2-2222-2-2-2-2220000-2200002-22-200000000-2-222-2-22200000000000000000000−2i2i−2i2i000000000000
χ4922-2-2-2-222-2-222222-2-22-2-2-2-2220000-220000-22-2200000000-2-22222-2-2000000000000000000002-2-22000000000000
χ5022-2-2-2-222-2-222222-2-22-2-2-2-2220000-220000-22-2200000000-2-22222-2-200000000000000000000-222-2000000000000
χ5122-2-2-2-222-2-2222-2-2222-2-2-2-22200002-20000-22-220000000022-2-2-2-2220000000000000000000000002-2-2200000000
χ5222-2-2-2-222-2-2222-2-2222-2-2-2-22200002-20000-22-220000000022-2-2-2-222000000000000000000000000-222-200000000
χ534444-4-4-4-44-4-4440000444-4-4-4-400000000004-4-440000000000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-44-20000-2-2-222220000000000-222-2−2i3−2i32i32i3−2i3−2i32i32i300000000000000000000000000000000000000000000
χ554444-4-4-4-44-4-44-20000-2-2-222220000000000-222-22i32i3−2i3−2i32i32i3−2i3−2i300000000000000000000000000000000000000000000
χ564444-4-4-4-4-444-440000444-4-4-4-40000000000-444-40000000000000000000000000000000000000000000000000000
χ574444-4-4-4-4-444-4-20000-2-2-2222200000000002-2-22−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000000
χ584444-4-4-4-4-444-4-20000-2-2-2222200000000002-2-222i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000000
χ5944-4-444-4-44-44-4-20000-222-2-2220000004i−4i4i−4i-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ6044-4-444-4-44-44-4-20000-222-2-222000000−4i4i−4i4i-2-22200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ6144-4-444-4-4-44-44-20000-222-2-2220000004i−4i−4i4i22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6244-4-444-4-4-44-44-20000-222-2-222000000−4i4i4i−4i22-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ6344-4-4-4-44444-4-4-244-4-4-22222-2-200004-40000-22-2200000000-2-222-2-222000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-2-4-444-22222-2-20000-440000-22-220000000022-2-222-2-2000000000000000000000000000000000000
χ6544-4-4-4-444-4-444-244-4-4-22222-2-20000-4400002-22-20000000022-2-2-2-222000000000000000000000000000000000000
χ6644-4-4-4-444-4-444-2-4-444-22222-2-200004-400002-22-200000000-2-22222-2-2000000000000000000000000000000000000
χ674-44-44-44-4000044i−4i4i−4i-44-44-44-4000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ684-44-44-44-400004−4i4i−4i4i-44-44-44-400000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ694-44-44-44-40000-24i−4i4i−4i2-22-22-2200000000000000−2i32i3−2i32i300000000−2i2i−2i2i000023−2323−230000000000000000000000000000
χ704-44-44-44-40000-24i−4i4i−4i2-22-22-22000000000000002i3−2i32i3−2i300000000−2i2i−2i2i0000−2323−23230000000000000000000000000000
χ714-44-44-44-40000-2−4i4i−4i4i2-22-22-2200000000000000−2i32i3−2i32i3000000002i−2i2i−2i0000−2323−23230000000000000000000000000000
χ724-44-44-44-40000-2−4i4i−4i4i2-22-22-22000000000000002i3−2i32i3−2i3000000002i−2i2i−2i000023−2323−230000000000000000000000000000
χ734-44-4-44-44000040000-44-4-44-444-40000000000004-4-44000000000000000000000000000000000000000000000000
χ744-44-4-44-44000040000-44-4-44-44-44000000000000-444-4000000000000000000000000000000000000000000000000
χ754-44-4-44-440000-200002-222-22-24-4000000000000-222-20000−2i32i3−2i32i30000−2i32i3−2i32i300000000000000000000000000000000
χ764-44-4-44-440000-200002-222-22-24-4000000000000-222-200002i3−2i32i3−2i300002i3−2i32i3−2i300000000000000000000000000000000
χ774-44-4-44-440000-200002-222-22-2-440000000000002-2-220000−2i32i3−2i32i300002i3−2i32i3−2i300000000000000000000000000000000
χ784-44-4-44-440000-200002-222-22-2-440000000000002-2-2200002i3−2i32i3−2i30000−2i32i3−2i32i300000000000000000000000000000000
χ794-4-444-4-44000040000-4-444-4-44004-4000000000000004-44-400000000000000000000000000000000000000000000
χ804-4-444-4-44000040000-4-444-4-4400-4400000000000000-44-4400000000000000000000000000000000000000000000
χ814-4-444-4-440000-2000022-2-222-2004-400000000000000-22-22−2i32i32i3−2i300000000−2i32i32i3−2i30000000000000000000000000000
χ824-4-444-4-440000-2000022-2-222-2004-400000000000000-22-222i3−2i3−2i32i3000000002i3−2i3−2i32i30000000000000000000000000000
χ834-4-444-4-440000-2000022-2-222-200-44000000000000002-22-2−2i32i32i3−2i3000000002i3−2i3−2i32i30000000000000000000000000000
χ844-4-444-4-440000-2000022-2-222-200-44000000000000002-22-22i3−2i3−2i32i300000000−2i32i32i3−2i30000000000000000000000000000
χ854-4-44-444-4000044i−4i−4i4i-4-44-444-4000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ864-4-44-444-400004−4i4i4i−4i-4-44-444-400000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ874-4-44-444-40000-24i−4i−4i4i22-22-2-22000000000000000000−2i32i32i3−2i30000−2i2i2i−2i23−23−232300000000000000000000000000000000
χ884-4-44-444-40000-24i−4i−4i4i22-22-2-220000000000000000002i3−2i3−2i32i30000−2i2i2i−2i−232323−2300000000000000000000000000000000
χ894-4-44-444-40000-2−4i4i4i−4i22-22-2-22000000000000000000−2i32i32i3−2i300002i−2i−2i2i−232323−2300000000000000000000000000000000
χ904-4-44-444-40000-2−4i4i4i−4i22-22-2-220000000000000000002i3−2i3−2i32i300002i−2i−2i2i23−23−232300000000000000000000000000000000

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