Finite Group Databasebeta

← Group #10845245

Character table — Group #10845245

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666444444121212121212121222444666688881212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ5111111111111111111111111-1-1111-1-1-1-11-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-111-1-11111-1-1-111-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-11-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1111-1-1111
χ7111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1111-1-111-1-111-1-1-1-1-1111
χ8111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11-1-11111-1-111111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ1111111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-111-1-1-1-1-11111-1-11
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1-11111111-1-1-1-111-1
χ17222222222-2-2-2-22222222000022-2-2-22222-200-20000000000-2-20000000000002222-2-2000000000-20000000
χ18222222222-2-2-2-22222222000022-2-2-22222-200-20000000000-2-2000000000000-2-2-2-22200000000020000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200200000000002200000000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000000022000000000000-2-22222000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-222111122-2-211-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-2-2-21111-2-22211-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22-2-211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-222-1-1-1-1-2-2221111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-2-1-1-1-122-2-2111111-1-1-1-11111000000211-1-1000000000000
χ2922-2-22-22-222-2-2222-22-2-2-22i2i−2i−2i002-2-2000020000000000000002i2i−2i−2i00000000000000000002-2000002i−2i000
χ3022-2-22-22-222-2-2222-22-2-2-22i2i−2i−2i002-2-2000020000000000000002i2i−2i−2i0000000000000000000-2200000−2i2i000
χ3122-2-22-22-222-2-2222-22-2-2-2−2i−2i2i2i002-2-200002000000000000000−2i−2i2i2i00000000000000000002-200000−2i2i000
χ3222-2-22-22-222-2-2222-22-2-2-2−2i−2i2i2i002-2-200002000000000000000−2i−2i2i2i0000000000000000000-22000002i−2i000
χ332-22-2-2-222222-2-2-2-222-2-222i−2i2i−2i0022-20000-20000000000000002i−2i2i−2i000000002-2002-200000002i−2i00000000
χ342-22-2-2-222222-2-2-2-222-2-222i−2i2i−2i0022-20000-20000000000000002i−2i2i−2i00000000-2200-220000000−2i2i00000000
χ352-22-2-2-222222-2-2-2-222-2-22−2i2i−2i2i0022-20000-2000000000000000−2i2i−2i2i000000002-2002-20000000−2i2i00000000
χ362-22-2-2-222222-2-2-2-222-2-22−2i2i−2i2i0022-20000-2000000000000000−2i2i−2i2i00000000-2200-2200000002i−2i00000000
χ372-22-2-2-2222-2-222-2-222-2-22000000-2-22000022-200022-2-20000000000000000002-200-2200000000002-200000
χ382-22-2-2-2222-2-222-2-222-2-22000000-2-22000022-200022-2-2000000000000000000-22002-20000000000-2200000
χ392-22-2-2-2222-2-222-2-222-2-22000000-2-2200002-22000-2-2220000000000000000002-200-220000000000-2200000
χ402-22-2-2-2222-2-222-2-222-2-22000000-2-2200002-22000-2-222000000000000000000-22002-200000000002-200000
χ412-2-22-222-222-22-2-2-2-2222-22-2-22002-220000-20002i−2i00002i−2i00002-2-222i2i−2i−2i000000000002i−2i00000000000000
χ422-2-22-222-222-22-2-2-2-2222-22-2-22002-220000-2000−2i2i0000−2i2i00002-2-22−2i−2i2i2i00000000000−2i2i00000000000000
χ432-2-22-222-222-22-2-2-2-2222-2-222-2002-220000-20002i−2i0000−2i2i0000-222-2−2i−2i2i2i000000000002i−2i00000000000000
χ442-2-22-222-222-22-2-2-2-2222-2-222-2002-220000-2000−2i2i00002i−2i0000-222-22i2i−2i−2i00000000000−2i2i00000000000000
χ452-2-22-222-2-12-22-2111-1-1-112-2-2200-11-1−i3−i3i3i310002i−2i−i3i3−i3i32i−2i00−i3i3-111-1−i−iii33−3−30000000−ii3−3000000000000
χ462-2-22-222-2-12-22-2111-1-1-112-2-2200-11-1−i3−i3i3i31000−2i2i−i3i3−i3i3−2i2i00−i3i3-111-1ii−i−i−3−3330000000i−i−33000000000000
χ472-2-22-222-2-12-22-2111-1-1-112-2-2200-11-1i3i3−i3−i310002i−2ii3−i3i3−i32i−2i00i3−i3-111-1−i−iii−3−3330000000−ii−33000000000000
χ482-2-22-222-2-12-22-2111-1-1-112-2-2200-11-1i3i3−i3−i31000−2i2ii3−i3i3−i3−2i2i00i3−i3-111-1ii−i−i33−3−30000000i−i3−3000000000000
χ492-2-22-222-2-12-22-2111-1-1-11-222-200-11-1−i3−i3i3i310002i−2ii3−i3i3−i3−2i2i00−i3i31-1-11ii−i−i−3−3330000000−ii3−3000000000000
χ502-2-22-222-2-12-22-2111-1-1-11-222-200-11-1−i3−i3i3i31000−2i2ii3−i3i3−i32i−2i00−i3i31-1-11−i−iii33−3−30000000i−i−33000000000000
χ512-2-22-222-2-12-22-2111-1-1-11-222-200-11-1i3i3−i3−i310002i−2i−i3i3−i3i3−2i2i00i3−i31-1-11ii−i−i33−3−30000000−ii−33000000000000
χ522-2-22-222-2-12-22-2111-1-1-11-222-200-11-1i3i3−i3−i31000−2i2i−i3i3−i3i32i−2i00i3−i31-1-11−i−iii−3−3330000000i−i3−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044222-2-2-2-2200-400000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222220040000000000-2-200000000000000000000000000000000000
χ554444-4-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000022−220
χ564444-4-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000−22220
χ5744-4-44-44-44-444-444-44-4-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ5844-4-44-44-4-24-4-44-2-22-22224i4i−4i−4i00-2220000-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ5944-4-44-44-4-24-4-44-2-22-2222−4i−4i4i4i00-2220000-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ6044-4-44-44-4-2-444-4-2-22-22220000002-2-20000200000−2i32i32i3−2i300000000000000000000000000000000000000000
χ6144-4-44-44-4-2-444-4-2-22-22220000002-2-200002000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ6244-4-4-44-44400004-4-4-4-44400004-40004-44-4000000000000000000000000000000000000000000000000000
χ6344-4-4-44-44400004-4-4-4-4440000-44000-44-44000000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-20000-22222-2-200004-4000-22-2200000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ6544-4-4-44-44-20000-22222-2-200004-4000-22-2200000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ6644-4-4-44-44-20000-22222-2-20000-440002-22-200000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ6744-4-4-44-44-20000-22222-2-20000-440002-22-200000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ684-44-444-4-440000-444-4-44-40000000000000000000000000−2i22i20000000000−2i22i22i2−2i200000000000000000000000
χ694-44-444-4-440000-444-4-44-400000000000000000000000002i2−2i200000000002i2−2i2−2i22i200000000000000000000000
χ704-44-444-4-4-200002-2-222-22000000000−2i32i32i3−2i3000000000000−2i22i2000000−666−6i2−i2−i2i200000000000000000000000
χ714-44-444-4-4-200002-2-222-22000000000−2i32i32i3−2i30000000000002i2−2i20000006−6−66−i2i2i2−i200000000000000000000000
χ724-44-444-4-4-200002-2-222-220000000002i3−2i3−2i32i3000000000000−2i22i20000006−6−66i2−i2−i2i200000000000000000000000
χ734-44-444-4-4-200002-2-222-220000000002i3−2i3−2i32i30000000000002i2−2i2000000−666−6−i2i2i2−i200000000000000000000000
χ744-44-4-4-444-244-4-422-2-222-24i−4i4i−4i00-2-2200002000000000000000−2i2i−2i2i0000000000000000000000000000000
χ754-44-4-4-444-244-4-422-2-222-2−4i4i−4i4i00-2-22000020000000000000002i−2i2i−2i0000000000000000000000000000000
χ764-44-4-4-444-2-4-44422-2-222-200000022-20000-24-4000-2-22200000000000000000000000000000000000000000
χ774-44-4-4-444-2-4-44422-2-222-200000022-20000-2-4400022-2-200000000000000000000000000000000000000000
χ784-4-444-4-4440000-44-4-44-4400000000000000000000000000000000000000000004-40000000000000000000
χ794-4-444-4-4440000-44-4-44-440000000000000000000000000000000000000000000-440000000000000000000
χ804-4-44-444-44-44-44-4-4-4444-4000000-44-40000400000000000000000000000000000000000000000000000000
χ814-4-44-444-4-2-44-44222-2-2-220000002-22−2i3−2i32i32i3-200000000000002i3−2i300000000000000000000000000000000000
χ824-4-44-444-4-2-44-44222-2-2-220000002-222i32i3−2i3−2i3-20000000000000−2i32i300000000000000000000000000000000000
χ838888-8-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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