Finite Group Databasebeta

← Group #10855118

Character table — Group #10855118

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
χ5111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-111-1-1-11111-1-111-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111-1-11
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111111-1-1-1-1-111-1-111-1-11
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-1111-1-111-1-111-1
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
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-111-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1111-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111111-1-1-111-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-1-1111111-1-1-1
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-22211-2-2221111-1-1-1-1-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-21122-2-21111-1-1-1-11111-1-1-1-10000002-1-111000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222221122-2-2-1-1-1-111111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-211-2-222-1-1-1-11111-1-1-1-111110000002-1-111000000000000
χ2922-2-22-2-222-22-2222-22-2-2-22i2i−2i−2i00-2-20000220002i−2i00002-200002i2i−2i−2i22-2-200000000000002i−2i000000000000
χ3022-2-22-2-222-22-2222-22-2-2-22i2i−2i−2i00-2-2000022000−2i2i0000-2200002i2i−2i−2i-2-2220000000000000−2i2i000000000000
χ3122-2-22-2-222-22-2222-22-2-2-2−2i−2i2i2i00-2-20000220002i−2i0000-220000−2i−2i2i2i-2-22200000000000002i−2i000000000000
χ3222-2-22-2-222-22-2222-22-2-2-2−2i−2i2i2i00-2-2000022000−2i2i00002-20000−2i−2i2i2i22-2-20000000000000−2i2i000000000000
χ3322-2-22-2-22-1-22-22-1-11-11112i2i−2i−2i0011−i3−i3i3i3-1-10002i−2i−i3i3002-233−3−3−i−iii-1-111−i3−i3i3i300000003−3−ii000000000000
χ3422-2-22-2-22-1-22-22-1-11-11112i2i−2i−2i0011−i3−i3i3i3-1-1000−2i2i−i3i300-2233−3−3−i−iii11-1-1i3i3−i3−i30000000−33i−i000000000000
χ3522-2-22-2-22-1-22-22-1-11-11112i2i−2i−2i0011i3i3−i3−i3-1-10002i−2ii3−i3002-2−3−333−i−iii-1-111i3i3−i3−i30000000−33−ii000000000000
χ3622-2-22-2-22-1-22-22-1-11-11112i2i−2i−2i0011i3i3−i3−i3-1-1000−2i2ii3−i300-22−3−333−i−iii11-1-1−i3−i3i3i300000003−3i−i000000000000
χ3722-2-22-2-22-1-22-22-1-11-1111−2i−2i2i2i0011−i3−i3i3i3-1-10002i−2i−i3i300-22−3−333ii−i−i11-1-1i3i3−i3−i300000003−3−ii000000000000
χ3822-2-22-2-22-1-22-22-1-11-1111−2i−2i2i2i0011−i3−i3i3i3-1-1000−2i2i−i3i3002-2−3−333ii−i−i-1-111−i3−i3i3i30000000−33i−i000000000000
χ3922-2-22-2-22-1-22-22-1-11-1111−2i−2i2i2i0011i3i3−i3−i3-1-10002i−2ii3−i300-2233−3−3ii−i−i11-1-1−i3−i3i3i30000000−33−ii000000000000
χ4022-2-22-2-22-1-22-22-1-11-1111−2i−2i2i2i0011i3i3−i3−i3-1-1000−2i2ii3−i3002-233−3−3ii−i−i-1-111i3i3−i3−i300000003−3i−i000000000000
χ412-222-2-2-2222-2-22-2-2222-2-22i−2i2i−2i002-200002-20000000000000002i−2i2i−2i000000002-2002-2000000002i−2i0000000
χ422-222-2-2-2222-2-22-2-2222-2-22i−2i2i−2i002-200002-20000000000000002i−2i2i−2i00000000-2200-2200000000−2i2i0000000
χ432-222-2-2-2222-2-22-2-2222-2-2−2i2i−2i2i002-200002-2000000000000000−2i2i−2i2i000000002-2002-200000000−2i2i0000000
χ442-222-2-2-2222-2-22-2-2222-2-2−2i2i−2i2i002-200002-2000000000000000−2i2i−2i2i00000000-2200-22000000002i−2i0000000
χ452-222-2-2-222-222-2-2-2222-2-2000000-220000-2202i−2i000000002i−2i2i−2i0000000000002-200-220000002i−2i000000000
χ462-222-2-2-222-222-2-2-2222-2-2000000-220000-2202i−2i000000002i−2i2i−2i000000000000-22002-2000000−2i2i000000000
χ472-222-2-2-222-222-2-2-2222-2-2000000-220000-220−2i2i00000000−2i2i−2i2i0000000000002-200-22000000−2i2i000000000
χ482-222-2-2-222-222-2-2-2222-2-2000000-220000-220−2i2i00000000−2i2i−2i2i000000000000-22002-20000002i−2i000000000
χ492-2-2-2-22222-2-222-2-2-22-2222-2-2200-2200002-20000000000000002-2-220000000000000000000000002-2002-20
χ502-2-2-2-22222-2-222-2-2-22-2222-2-2200-2200002-20000000000000002-2-22000000000000000000000000-2200-220
χ512-2-2-2-22222-2-222-2-2-22-222-222-200-2200002-2000000000000000-222-20000000000000000000000002-200-220
χ522-2-2-2-22222-2-222-2-2-22-222-222-200-2200002-2000000000000000-222-2000000000000000000000000-22002-20
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
χ55444-4-44-4-4400004-44-4-44-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-44-4-4400004-44-4-44-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-44-4-44-4400004-4-4-44-4400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ5844-44-4-44-4400004-4-4-44-44000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ5944-4-44-4-4444-44-444-44-4-4-4000000440000-4-400000000000000000000000000000000000000000000000000
χ6044-4-44-4-44-24-44-4-2-22-2222000000-2-2−2i3−2i32i32i322000002i3−2i30000000000000000000000000000000000000000000
χ6144-4-44-4-44-24-44-4-2-22-2222000000-2-22i32i3−2i3−2i32200000−2i32i30000000000000000000000000000000000000000000
χ624-444-4-4-44-24-4-4422-2-2-2224i−4i4i−4i00-220000-22000000000000000−2i2i−2i2i0000000000000000000000000000000
χ634-444-4-4-44-24-4-4422-2-2-222−4i4i−4i4i00-220000-220000000000000002i−2i2i−2i0000000000000000000000000000000
χ644-444-4-4-44-2-444-422-2-2-2220000002-200002-204i−4i00000000−2i2i−2i2i00000000000000000000000000000000000
χ654-444-4-4-44-2-444-422-2-2-2220000002-200002-20−4i4i000000002i−2i2i−2i00000000000000000000000000000000000
χ664-44-44-44-440000-444-4-4-4400004i−4i004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ674-44-44-44-440000-444-4-4-440000−4i4i00−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-200002-2-2222-200004i−4i00−2i2i−2i2i000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ694-44-44-44-4-200002-2-2222-200004i−4i00−2i2i−2i2i000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ704-44-44-44-4-200002-2-2222-20000−4i4i002i−2i2i−2i000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ714-44-44-44-4-200002-2-2222-20000−4i4i002i−2i2i−2i000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ724-4-4444-4-440000-44-4-444-4000000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000000
χ734-4-4444-4-440000-44-4-444-40000000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000
χ744-4-4444-4-4-200002-222-2-220000000023−23−2323000000000−2i22i20000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ754-4-4444-4-4-200002-222-2-220000000023−23−23230000000002i2−2i20000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ764-4-4444-4-4-200002-222-2-2200000000−232323−23000000000−2i22i20000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ774-4-4444-4-4-200002-222-2-2200000000−232323−230000000002i2−2i20000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ784-4-4-4-4444444-4-4-4-4-44-4440000004-40000-4400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-244-4-4222-22-2-2000000-2200002-200000000000−2i32i32i3−2i300000000000000000000000000000000000
χ804-4-4-4-4444-244-4-4222-22-2-2000000-2200002-2000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ814-4-4-4-4444-2-4-444222-22-2-24-4-44002-20000-22000000000000000-222-20000000000000000000000000000000
χ824-4-4-4-4444-2-4-444222-22-2-2-444-4002-20000-220000000000000002-2-220000000000000000000000000000000
χ83888-8-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-88-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000

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