Finite Group Databasebeta

← Group #10690943

Character table — Group #10690943

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
χ372222-2-2-2-222-2-220000222-2-2-2-22-22-200000022-2-222-2-222-2-20000000000000000000000000000000000002−22−22−22−2
χ382222-2-2-2-222-2-220000222-2-2-2-22-22-200000022-2-222-2-222-2-2000000000000000000000000000000000000−22−22−22−22
χ392222-2-2-2-222-2-220000222-2-2-2-2-22-2200000022-2-2-2-222-2-2220000000000000000000000000000000000002−22−2−22−22
χ402222-2-2-2-222-2-220000222-2-2-2-2-22-2200000022-2-2-2-222-2-222000000000000000000000000000000000000−22−222−22−2
χ412222-2-2-2-2-2-22220000222-2-2-2-22-2-22000000-2-22222-2-2-2-222000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ422222-2-2-2-2-2-22220000222-2-2-2-22-2-22000000-2-22222-2-2-2-222000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ432222-2-2-2-2-2-22220000222-2-2-2-2-222-2000000-2-222-2-22222-2-2000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ442222-2-2-2-2-2-22220000222-2-2-2-2-222-2000000-2-222-2-22222-2-2000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ4522-2-22-2-222-22-2222-2-22-2-22-2-2200002-200002-22-20000000022-2-222-2-20000000000000000000000002i−2i2i−2i00000000
χ4622-2-22-2-222-22-2222-2-22-2-22-2-2200002-200002-22-20000000022-2-222-2-2000000000000000000000000−2i2i−2i2i00000000
χ4722-2-22-2-222-22-22-2-2222-2-22-2-220000-2200002-22-200000000-2-222-2-222000000000000000000002i−2i2i−2i000000000000
χ4822-2-22-2-222-22-22-2-2222-2-22-2-220000-2200002-22-200000000-2-222-2-22200000000000000000000−2i2i−2i2i000000000000
χ4922-2-22-2-22-22-22222-2-22-2-22-2-220000-220000-22-2200000000-2-22222-2-2000000000000000000002-2-22000000000000
χ5022-2-22-2-22-22-22222-2-22-2-22-2-220000-220000-22-2200000000-2-22222-2-200000000000000000000-222-2000000000000
χ5122-2-22-2-22-22-222-2-2222-2-22-2-2200002-20000-22-220000000022-2-2-2-2220000000000000000000000002-2-2200000000
χ5222-2-22-2-22-22-222-2-2222-2-22-2-2200002-20000-22-220000000022-2-2-2-222000000000000000000000000-222-200000000
χ534444-4-4-4-444-4-4-20000-2-2-222224-44-4000000-2-222-2-222-2-22200000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4-20000-2-2-22222-44-44000000-2-22222-2-222-2-200000000000000000000000000000000000000000000
χ554444-4-4-4-4-4-444-20000-2-2-222224-4-4400000022-2-2-2-22222-2-200000000000000000000000000000000000000000000
χ564444-4-4-4-4-4-444-20000-2-2-22222-444-400000022-2-222-2-2-2-22200000000000000000000000000000000000000000000
χ5744-4-44-4-444-44-4-244-4-4-222-222-200004-40000-22-2200000000-2-222-2-222000000000000000000000000000000000000
χ5844-4-44-4-444-44-4-2-4-444-222-222-20000-440000-22-220000000022-2-222-2-2000000000000000000000000000000000000
χ5944-4-44-4-44-44-44-244-4-4-222-222-20000-4400002-22-20000000022-2-2-2-222000000000000000000000000000000000000
χ6044-4-44-4-44-44-44-2-4-444-222-222-200004-400002-22-200000000-2-22222-2-2000000000000000000000000000000000000
χ6144-4-4-444-44-4-44400004-4-4-444-400000000004-4-440000000000000000000000000000000000000000000000000000
χ6244-4-4-444-44-4-44-20000-2222-2-220000000000-222-200000000000000002323−23−232323−23−230000000000000000000000000000
χ6344-4-4-444-44-4-44-20000-2222-2-220000000000-222-20000000000000000−23−232323−23−2323230000000000000000000000000000
χ6444-4-4-444-4-444-4400004-4-4-444-40000000000-444-40000000000000000000000000000000000000000000000000000
χ6544-4-4-444-4-444-4-20000-2222-2-2200000000002-2-2200000000000000002323−23−23−23−2323230000000000000000000000000000
χ6644-4-4-444-4-444-4-20000-2222-2-2200000000002-2-220000000000000000−23−2323232323−23−230000000000000000000000000000
χ674-44-444-4-4000044i−4i4i−4i-44-444-4-4000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ684-44-444-4-400004−4i4i−4i4i-44-444-4-400000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ694-44-444-4-40000-24i−4i4i−4i2-22-2-22200000000000000−2i32i3−2i32i300000000−2i2i−2i2i000023−2323−230000000000000000000000000000
χ704-44-444-4-40000-24i−4i4i−4i2-22-2-222000000000000002i3−2i32i3−2i300000000−2i2i−2i2i0000−2323−23230000000000000000000000000000
χ714-44-444-4-40000-2−4i4i−4i4i2-22-2-22200000000000000−2i32i3−2i32i3000000002i−2i2i−2i0000−2323−23230000000000000000000000000000
χ724-44-444-4-40000-2−4i4i−4i4i2-22-2-222000000000000002i3−2i32i3−2i3000000002i−2i2i−2i000023−2323−230000000000000000000000000000
χ734-44-4-4-444000040000-44-4-4-4440000004-400000000000000000000004-44-400000000000000000000000000000000
χ744-44-4-4-444000040000-44-4-4-444000000-440000000000000000000000-44-4400000000000000000000000000000000
χ754-44-4-4-4440000-200002-2222-2-20000004-4000000−2i32i32i3−2i30000−2i32i3−2i32i30000-22-2200000000000000000000000000000000
χ764-44-4-4-4440000-200002-2222-2-20000004-40000002i3−2i3−2i32i300002i3−2i32i3−2i30000-22-2200000000000000000000000000000000
χ774-44-4-4-4440000-200002-2222-2-2000000-44000000−2i32i32i3−2i300002i3−2i32i3−2i300002-22-200000000000000000000000000000000
χ784-44-4-4-4440000-200002-2222-2-2000000-440000002i3−2i3−2i32i30000−2i32i3−2i32i300002-22-200000000000000000000000000000000
χ794-4-444-44-4000044i−4i−4i4i-4-444-44-4000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ804-4-444-44-400004−4i4i4i−4i-4-444-44-400000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ814-4-444-44-40000-24i−4i−4i4i22-2-22-22000000000000000000−2i32i3−2i32i30000−2i2i2i−2i23−23−232300000000000000000000000000000000
χ824-4-444-44-40000-24i−4i−4i4i22-2-22-220000000000000000002i3−2i32i3−2i30000−2i2i2i−2i−232323−2300000000000000000000000000000000
χ834-4-444-44-40000-2−4i4i4i−4i22-2-22-22000000000000000000−2i32i3−2i32i300002i−2i−2i2i−232323−2300000000000000000000000000000000
χ844-4-444-44-40000-2−4i4i4i−4i22-2-22-220000000000000000002i3−2i32i3−2i300002i−2i−2i2i23−23−232300000000000000000000000000000000
χ854-4-44-44-44000040000-4-44-44-44000000004-40000000000000000000000004-4-440000000000000000000000000000
χ864-4-44-44-44000040000-4-44-44-4400000000-44000000000000000000000000-444-40000000000000000000000000000
χ874-4-44-44-440000-2000022-22-22-2000000004-400000000−2i32i32i3−2i3−2i32i32i3−2i300000000-222-20000000000000000000000000000
χ884-4-44-44-440000-2000022-22-22-2000000004-4000000002i3−2i3−2i32i32i3−2i3−2i32i300000000-222-20000000000000000000000000000
χ894-4-44-44-440000-2000022-22-22-200000000-4400000000−2i32i32i3−2i32i3−2i3−2i32i3000000002-2-220000000000000000000000000000
χ904-4-44-44-440000-2000022-22-22-200000000-44000000002i3−2i3−2i32i3−2i32i32i3−2i3000000002-2-220000000000000000000000000000

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