Finite Group Databasebeta

← Group #10694269

Character table — Group #10694269

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666444444444412121212121212121212121212121212121212121212121212121212444412121212121212128888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-222-2-2222222222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-222-2-22222222-2-222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ19222222222-2-222-2-222222222222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-222-2-2222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-11111111111111111-1-1-1-122-2-2-1-1-1-111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-2-2221111-1-1-1-10000000000000000
χ2522222222-122-2-222-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2622222222-122-2-222-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2722222222-122-2-222-2-2-1-1-1-1-1-1-1-2-222-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2822222222-122-2-222-2-2-1-1-1-1-1-1-1-2-222-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2922222222-1-2-222-2-222-1-1-1-1-1-1-122-2-2-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ3022222222-1-2-222-2-222-1-1-1-1-1-1-122-2-2-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ3122222222-1-2-222-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ3222222222-1-2-222-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-12-22-2-1-111-1-1110000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-22-2211-1-111-1-10000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-12-2-22-1-11111-1-10000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-222-211-1-1-1-1110000000000000000
χ372222-2-2-2-22002200-2-2222-2-2-2-2002-22-20000000022-2-2000022-2-222-2-2000000000000000000002−22−22−22−200000000
χ382222-2-2-2-22002200-2-2222-2-2-2-2002-22-20000000022-2-2000022-2-222-2-200000000000000000000−22−22−22−2200000000
χ392222-2-2-2-22002200-2-2222-2-2-2-200-22-220000000022-2-20000-2-222-2-222000000000000000000002−22−2−22−2200000000
χ402222-2-2-2-22002200-2-2222-2-2-2-200-22-220000000022-2-20000-2-222-2-22200000000000000000000−22−222−22−200000000
χ412222-2-2-2-2200-2-20022222-2-2-2-2002-2-2200000000-2-222000022-2-2-2-22200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ422222-2-2-2-2200-2-20022222-2-2-2-2002-2-2200000000-2-222000022-2-2-2-22200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ432222-2-2-2-2200-2-20022222-2-2-2-200-222-200000000-2-2220000-2-22222-2-200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ442222-2-2-2-2200-2-20022222-2-2-2-200-222-200000000-2-2220000-2-22222-2-200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ4522-2-22-2-222222-2-2-22-22-2-22-2-22000000002-222-2-22-22-2000000000000000022-2-20000000000000000000000002i−2i2i−2i
χ4622-2-22-2-222222-2-2-22-22-2-22-2-22000000002-222-2-22-22-2000000000000000022-2-2000000000000000000000000−2i2i−2i2i
χ4722-2-22-2-22222-22-2-2-222-2-22-2-2200000000-2222-2-2-22-220000000000000000-2-222000000000000000000002i−2i2i−2i0000
χ4822-2-22-2-22222-22-2-2-222-2-22-2-2200000000-2222-2-2-22-220000000000000000-2-22200000000000000000000−2i2i−2i2i0000
χ4922-2-22-2-222-2-22-2222-22-2-22-2-2200000000-22-2-2222-22-20000000000000000-2-222000000000000000000002-2-220000
χ5022-2-22-2-222-2-22-2222-22-2-22-2-2200000000-22-2-2222-22-20000000000000000-2-22200000000000000000000-222-20000
χ5122-2-22-2-222-2-2-2222-222-2-22-2-22000000002-2-2-222-22-22000000000000000022-2-20000000000000000000000002-2-22
χ5222-2-22-2-222-2-2-2222-222-2-22-2-22000000002-2-2-222-22-22000000000000000022-2-2000000000000000000000000-222-2
χ534444-4-4-4-4-2004400-4-4-2-2-22222004-44-400000000-2-2220000-2-222-2-222000000000000000000000000000000000000
χ544444-4-4-4-4-2004400-4-4-2-2-2222200-44-4400000000-2-222000022-2-222-2-2000000000000000000000000000000000000
χ554444-4-4-4-4-200-4-40044-2-2-22222004-4-440000000022-2-20000-2-22222-2-2000000000000000000000000000000000000
χ564444-4-4-4-4-200-4-40044-2-2-2222200-444-40000000022-2-2000022-2-2-2-222000000000000000000000000000000000000
χ5744-4-44-4-44-2444-4-4-44-4-222-222-2000000004-4-2-222-22-220000000000000000-2-2220000000000000000000000000000
χ5844-4-44-4-44-244-44-4-4-44-222-222-200000000-44-2-2222-22-2000000000000000022-2-20000000000000000000000000000
χ5944-4-44-4-44-2-4-44-4444-4-222-222-200000000-4422-2-2-22-22000000000000000022-2-20000000000000000000000000000
χ6044-4-44-4-44-2-4-4-4444-44-222-222-2000000004-422-2-22-22-20000000000000000-2-2220000000000000000000000000000
χ6144-4-4-444-44004-400-444-4-4-444-4000000000000004-4-44000000000000000000000000000000000000000000000000
χ6244-4-4-444-4400-44004-44-4-4-444-400000000000000-444-4000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-2004-400-44-2222-2-2200000000000000-222-2−2i3−2i32i32i300000000−2i3−2i32i32i300000000000000000000000000000000
χ6444-4-4-444-4-2004-400-44-2222-2-2200000000000000-222-22i32i3−2i3−2i3000000002i32i3−2i3−2i300000000000000000000000000000000
χ6544-4-4-444-4-200-44004-4-2222-2-22000000000000002-2-22−2i3−2i32i32i3000000002i32i3−2i3−2i300000000000000000000000000000000
χ6644-4-4-444-4-200-44004-4-2222-2-22000000000000002-2-222i32i3−2i3−2i300000000−2i3−2i32i32i300000000000000000000000000000000
χ674-44-444-4-444-4004-400-44-444-4-400000000004-44-40000000000000000000000000000000000000000000000000000
χ684-44-444-4-44-4400-4400-44-444-4-40000000000-44-440000000000000000000000000000000000000000000000000000
χ694-44-444-4-4-24-4004-4002-22-2-2220000000000-22-220000−2i32i3−2i32i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ704-44-444-4-4-24-4004-4002-22-2-2220000000000-22-2200002i3−2i32i3−2i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ714-44-444-4-4-2-4400-44002-22-2-22200000000002-22-20000−2i32i3−2i32i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ724-44-444-4-4-2-4400-44002-22-2-22200000000002-22-200002i3−2i32i3−2i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ734-44-4-4-444400000000-44-4-4-4440000004-400000000000000000000004-44-400000000000000000000000000000000
χ744-44-4-4-444400000000-44-4-4-444000000-440000000000000000000000-44-4400000000000000000000000000000000
χ754-44-4-4-444-2000000002-2222-2-20000004-4000000000000000000−2i32i32i3−2i3-22-22−2i32i3−2i32i30000000000000000000000000000
χ764-44-4-4-444-2000000002-2222-2-20000004-40000000000000000002i3−2i3−2i32i3-22-222i3−2i32i3−2i30000000000000000000000000000
χ774-44-4-4-444-2000000002-2222-2-2000000-44000000000000000000−2i32i32i3−2i32-22-22i3−2i32i3−2i30000000000000000000000000000
χ784-44-4-4-444-2000000002-2222-2-2000000-440000000000000000002i3−2i3−2i32i32-22-2−2i32i3−2i32i30000000000000000000000000000
χ794-4-444-44-444-400-4400-4-444-44-400000000004-4-440000000000000000000000000000000000000000000000000000
χ804-4-444-44-44-44004-400-4-444-44-40000000000-444-40000000000000000000000000000000000000000000000000000
χ814-4-444-44-4-24-400-440022-2-22-220000000000-222-200000000−2i32i3−2i32i30000−2i32i32i3−2i300000000000000000000000000000000
χ824-4-444-44-4-24-400-440022-2-22-220000000000-222-2000000002i3−2i32i3−2i300002i3−2i3−2i32i300000000000000000000000000000000
χ834-4-444-44-4-2-44004-40022-2-22-2200000000002-2-2200000000−2i32i3−2i32i300002i3−2i3−2i32i300000000000000000000000000000000
χ844-4-444-44-4-2-44004-40022-2-22-2200000000002-2-22000000002i3−2i32i3−2i30000−2i32i32i3−2i300000000000000000000000000000000
χ854-4-44-44-44400000000-4-44-44-444-400000000000000004-4-4400000000000000000000000000000000000000000000
χ864-4-44-44-44400000000-4-44-44-44-440000000000000000-444-400000000000000000000000000000000000000000000
χ874-4-44-44-44-20000000022-22-22-24-40000000000000000-222-2−2i32i32i3−2i3000000002i3−2i3−2i32i30000000000000000000000000000
χ884-4-44-44-44-20000000022-22-22-24-40000000000000000-222-22i3−2i3−2i32i300000000−2i32i32i3−2i30000000000000000000000000000
χ894-4-44-44-44-20000000022-22-22-2-4400000000000000002-2-22−2i32i32i3−2i300000000−2i32i32i3−2i30000000000000000000000000000
χ904-4-44-44-44-20000000022-22-22-2-4400000000000000002-2-222i3−2i3−2i32i3000000002i3−2i3−2i32i30000000000000000000000000000

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