Finite Group Databasebeta

← Group #10855058

Character table — Group #10855058

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122444466888812121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1-111-1-1-11111-1-111-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111-1-11
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-111-1-111-1-11
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-1111-1-111-1-111-1
χ911111111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1111-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111111-1-1-111-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-11-1-1111111-1-1-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-20000-2-20000000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-20000-2-200000000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-22000022000000000000000000002222-2-200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200002200000000000000000000-2-2-2-22200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-22211-2-222-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-21122-2-2-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-222-1-1-2-2-2-211111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222221122-2-21111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-211-2-2221111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-2-2-222-22-22-2222-22-2-2-22i2i−2i−2i00-2-20000220002i−2i00002-22i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ3022-2-2-222-22-22-2222-22-2-2-22i2i−2i−2i00-2-2000022000−2i2i0000-222i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ3122-2-2-222-22-22-2222-22-2-2-2−2i−2i2i2i00-2-20000220002i−2i0000-22−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ3222-2-2-222-22-22-2222-22-2-2-2−2i−2i2i2i00-2-2000022000−2i2i00002-2−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ3322-2-2-222-2-1-22-22-1-11-11112i2i−2i−2i0011−i3−i3i3i3-1-10002i−2i−i3i3002-2−i−iii33−3−3-1-111−i3−i3i3i300000003−3−ii000000000000
χ3422-2-2-222-2-1-22-22-1-11-11112i2i−2i−2i0011−i3−i3i3i3-1-1000−2i2i−i3i300-22−i−iii33−3−311-1-1i3i3−i3−i30000000−33i−i000000000000
χ3522-2-2-222-2-1-22-22-1-11-11112i2i−2i−2i0011i3i3−i3−i3-1-10002i−2ii3−i3002-2−i−iii−3−333-1-111i3i3−i3−i30000000−33−ii000000000000
χ3622-2-2-222-2-1-22-22-1-11-11112i2i−2i−2i0011i3i3−i3−i3-1-1000−2i2ii3−i300-22−i−iii−3−33311-1-1−i3−i3i3i300000003−3i−i000000000000
χ3722-2-2-222-2-1-22-22-1-11-1111−2i−2i2i2i0011−i3−i3i3i3-1-10002i−2i−i3i300-22ii−i−i−3−33311-1-1i3i3−i3−i300000003−3−ii000000000000
χ3822-2-2-222-2-1-22-22-1-11-1111−2i−2i2i2i0011−i3−i3i3i3-1-1000−2i2i−i3i3002-2ii−i−i−3−333-1-111−i3−i3i3i30000000−33i−i000000000000
χ3922-2-2-222-2-1-22-22-1-11-1111−2i−2i2i2i0011i3i3−i3−i3-1-10002i−2ii3−i300-22ii−i−i33−3−311-1-1−i3−i3i3i30000000−33−ii000000000000
χ4022-2-2-222-2-1-22-22-1-11-1111−2i−2i2i2i0011i3i3−i3−i3-1-1000−2i2ii3−i3002-2ii−i−i33−3−3-1-111i3i3−i3−i300000003−3i−i000000000000
χ412-22-2-2-2222-2-222-2-2-222-222-22-2002-200002-2000000000002-22-200000000000000000000000000002-2002-20
χ422-22-2-2-2222-2-222-2-2-222-222-22-2002-200002-2000000000002-22-20000000000000000000000000000-2200-220
χ432-22-2-2-2222-2-222-2-2-222-22-22-22002-200002-200000000000-22-2200000000000000000000000000002-200-220
χ442-22-2-2-2222-2-222-2-2-222-22-22-22002-200002-200000000000-22-220000000000000000000000000000-22002-20
χ452-2-222-22-222-2-22-2-222-22-22i−2i−2i2i00-2200002-2000000000002i−2i−2i2i0000000000002-2002-2000000002i−2i0000000
χ462-2-222-22-222-2-22-2-222-22-22i−2i−2i2i00-2200002-2000000000002i−2i−2i2i000000000000-2200-2200000000−2i2i0000000
χ472-2-222-22-222-2-22-2-222-22-2−2i2i2i−2i00-2200002-200000000000−2i2i2i−2i0000000000002-2002-200000000−2i2i0000000
χ482-2-222-22-222-2-22-2-222-22-2−2i2i2i−2i00-2200002-200000000000−2i2i2i−2i000000000000-2200-22000000002i−2i0000000
χ492-2-222-22-22-222-2-2-222-22-20000002-20000-2202i−2i0000000000002i−2i2i−2i000000002-200-220000002i−2i000000000
χ502-2-222-22-22-222-2-2-222-22-20000002-20000-2202i−2i0000000000002i−2i2i−2i00000000-22002-2000000−2i2i000000000
χ512-2-222-22-22-222-2-2-222-22-20000002-20000-220−2i2i000000000000−2i2i−2i2i000000002-200-22000000−2i2i000000000
χ522-2-222-22-22-222-2-2-222-22-20000002-20000-220−2i2i000000000000−2i2i−2i2i00000000-22002-20000002i−2i000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000220000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222240000-2-20000000000000000000000000000000000000000000
χ55444-44-4-4-4400004-4-4-444-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ56444-44-4-4-4400004-4-4-444-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ57444-44-4-4-4-20000-2222-2-220000000023−2323−2300000000022−2200000000006−66−6−22−2200000000000000000000000
χ58444-44-4-4-4-20000-2222-2-220000000023−2323−23000000000−22220000000000−66−662−22−200000000000000000000000
χ59444-44-4-4-4-20000-2222-2-2200000000−2323−232300000000022−220000000000−66−66−22−2200000000000000000000000
χ60444-44-4-4-4-20000-2222-2-2200000000−2323−2323000000000−222200000000006−66−62−22−200000000000000000000000
χ6144-44-4-4-44400004-44-4-4-4400004i−4i004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6244-44-4-4-44400004-44-4-4-440000−4i4i00−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ6344-44-4-4-44-20000-22-2222-200004i−4i00−2i2i2i−2i0000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ6444-44-4-4-44-20000-22-2222-200004i−4i00−2i2i2i−2i000000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ6544-44-4-4-44-20000-22-2222-20000−4i4i002i−2i−2i2i0000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ6644-44-4-4-44-20000-22-2222-20000−4i4i002i−2i−2i2i000000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ6744-4-4-444-444-44-444-44-4-4-4000000440000-4-400000000000000000000000000000000000000000000000000
χ6844-4-4-444-4-24-44-4-2-22-2222000000-2-2−2i3−2i32i32i322000002i3−2i30000000000000000000000000000000000000000000
χ6944-4-4-444-4-24-44-4-2-22-2222000000-2-22i32i3−2i3−2i32200000−2i32i30000000000000000000000000000000000000000000
χ704-444-44-4-440000-444-44-4-400000000000000000000000000000000000000000004-40000000000000000000
χ714-444-44-4-440000-444-44-4-40000000000000000000000000000000000000000000-440000000000000000000
χ724-44-4-4-444444-4-4-4-4-444-44000000-440000-4400000000000000000000000000000000000000000000000000
χ734-44-4-4-444-244-4-4222-2-22-20000002-200002-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ744-44-4-4-444-244-4-4222-2-22-20000002-200002-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ754-44-4-4-444-2-4-444222-2-22-24-44-400-220000-2200000000000-22-2200000000000000000000000000000000000
χ764-44-4-4-444-2-4-444222-2-22-2-44-4400-220000-22000000000002-22-200000000000000000000000000000000000
χ774-4-444-44-4-24-4-4422-2-22-224i−4i−4i4i002-20000-2200000000000−2i2i2i−2i00000000000000000000000000000000000
χ784-4-444-44-4-24-4-4422-2-22-22−4i4i4i−4i002-20000-22000000000002i−2i−2i2i00000000000000000000000000000000000
χ794-4-444-44-4-2-444-422-2-22-22000000-2200002-204i−4i000000000000−2i2i−2i2i0000000000000000000000000000000
χ804-4-444-44-4-2-444-422-2-22-22000000-2200002-20−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000
χ814-4-4-444-4440000-44-4-4-4440000000000000000000000000000000000000000000000000000000000022−22000
χ824-4-4-444-4440000-44-4-4-44400000000000000000000000000000000000000000000000000000000000−2222000
χ838-888-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000

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