Finite Group Databasebeta

← Group #10855141

Character table — Group #10855141

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212124444488881212121212121212121224242424242424242244442661212244444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-111-1
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-111-1-11
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-111-1-111-1-11
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-111-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-1-111-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-1111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-200000000-2-2000000000000000022-2-22200000-200000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-200000000-2-20000000000000000-2-222-2-200000200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000000022000000000000000022-2-2-2-200000200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-2222200000-200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-222-2-22211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2222222-2-2111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-2-2-222111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-222-2-2-22-2-22222-2-22-2-2002i2i−2i−2i2-200002-20002i−2i002-2002i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ3022-222-2-2-22-2-22222-2-22-2-2002i2i−2i−2i2-200002-2000−2i2i00-22002i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ3122-222-2-2-22-2-22222-2-22-2-200−2i−2i2i2i2-200002-20002i−2i00-2200−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ3222-222-2-2-22-2-22222-2-22-2-200−2i−2i2i2i2-200002-2000−2i2i002-200−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ3322-222-2-2-2-1-2-222-1-111-111002i2i−2i−2i-1133−3−3-110002i−2i002-23−3−i−iii−i3−i3i3i3-1-11133−3−30000000−i3i3−ii000000000000
χ3422-222-2-2-2-1-2-222-1-111-111002i2i−2i−2i-1133−3−3-11000−2i2i00-223−3−i−iii−i3−i3i3i311-1-1−3−3330000000i3−i3i−i000000000000
χ3522-222-2-2-2-1-2-222-1-111-111002i2i−2i−2i-11−3−333-110002i−2i002-2−33−i−iiii3i3−i3−i3-1-111−3−3330000000i3−i3−ii000000000000
χ3622-222-2-2-2-1-2-222-1-111-111002i2i−2i−2i-11−3−333-11000−2i2i00-22−33−i−iiii3i3−i3−i311-1-133−3−30000000−i3i3i−i000000000000
χ3722-222-2-2-2-1-2-222-1-111-11100−2i−2i2i2i-1133−3−3-110002i−2i00-223−3ii−i−ii3i3−i3−i311-1-1−3−3330000000−i3i3−ii000000000000
χ3822-222-2-2-2-1-2-222-1-111-11100−2i−2i2i2i-1133−3−3-11000−2i2i002-23−3ii−i−ii3i3−i3−i3-1-11133−3−30000000i3−i3i−i000000000000
χ3922-222-2-2-2-1-2-222-1-111-11100−2i−2i2i2i-11−3−333-110002i−2i00-22−33ii−i−i−i3−i3i3i311-1-133−3−30000000i3−i3−ii000000000000
χ4022-222-2-2-2-1-2-222-1-111-11100−2i−2i2i2i-11−3−333-11000−2i2i002-2−33ii−i−i−i3−i3i3i3-1-111−3−3330000000−i3i3i−i000000000000
χ412-22-222-2-222-2-22-2222-2-2-2002i−2i2i−2i-2200002-2000000000002i−2i2i−2i0000000000002-22-200000000002i−2i0000000
χ422-22-222-2-222-2-22-2222-2-2-2002i−2i2i−2i-2200002-2000000000002i−2i2i−2i000000000000-22-220000000000−2i2i0000000
χ432-22-222-2-222-2-22-2222-2-2-200−2i2i−2i2i-2200002-200000000000−2i2i−2i2i0000000000002-22-20000000000−2i2i0000000
χ442-22-222-2-222-2-22-2222-2-2-200−2i2i−2i2i-2200002-200000000000−2i2i−2i2i000000000000-22-2200000000002i−2i0000000
χ452-22-222-2-22-222-2-2222-2-2-20000002-20000-2202i−2i0000000000002i−2i2i−2i000000002-2-22000000002i−2i000000000
χ462-22-222-2-22-222-2-2222-2-2-20000002-20000-2202i−2i0000000000002i−2i2i−2i00000000-222-200000000−2i2i000000000
χ472-22-222-2-22-222-2-2222-2-2-20000002-20000-220−2i2i000000000000−2i2i−2i2i000000002-2-2200000000−2i2i000000000
χ482-22-222-2-22-222-2-2222-2-2-20000002-20000-220−2i2i000000000000−2i2i−2i2i00000000-222-2000000002i−2i000000000
χ492-2-2-22-2222-22-22-22-2-2-222002-2-22-2-2000022000000000002-2-2200000000000000000000000000002-2002-20
χ502-2-2-22-2222-22-22-22-2-2-222002-2-22-2-2000022000000000002-2-220000000000000000000000000000-2200-220
χ512-2-2-22-2222-22-22-22-2-2-22200-222-2-2-200002200000000000-222-200000000000000000000000000002-200-220
χ522-2-2-22-2222-22-22-22-2-2-22200-222-2-2-200002200000000000-222-20000000000000000000000000000-22002-20
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-4-4-44400004-44-4-44-44i−4i0000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ56444-4-4-4-44400004-44-4-44-4−4i4i000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ57444-4-4-4-44-20000-22-222-224i−4i000000−2i2i−2i2i0000000000000000000006−66−6i6−i6i6−i600000000000000000000000
χ58444-4-4-4-44-20000-22-222-224i−4i000000−2i2i−2i2i000000000000000000000−66−66−i6i6−i6i600000000000000000000000
χ59444-4-4-4-44-20000-22-222-22−4i4i0000002i−2i2i−2i0000000000000000000006−66−6−i6i6−i6i600000000000000000000000
χ60444-4-4-4-44-20000-22-222-22−4i4i0000002i−2i2i−2i000000000000000000000−66−66i6−i6i6−i600000000000000000000000
χ6144-444-4-4-4444-4-444-4-44-4-4000000-440000-4400000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-244-4-4-2-222-2220000002-22323−23−232-2000000000−2323000000000000000000000000000000000000000
χ6344-444-4-4-4-244-4-4-2-222-2220000002-2−23−2323232-200000000023−23000000000000000000000000000000000000000
χ6444-4-4-444-4400004-4-44-4-440000000000000000000−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000
χ6544-4-4-444-4400004-4-44-4-4400000000000000000002i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000
χ6644-4-4-444-4-20000-222-222-200000000−2i32i32i3−2i30000000−2i22i2000000000000−666−6i2−i2−i2i200000000000000000000000
χ6744-4-4-444-4-20000-222-222-200000000−2i32i32i3−2i300000002i2−2i20000000000006−6−66−i2i2i2−i200000000000000000000000
χ6844-4-4-444-4-20000-222-222-2000000002i3−2i3−2i32i30000000−2i22i20000000000006−6−66i2−i2−i2i200000000000000000000000
χ6944-4-4-444-4-20000-222-222-2000000002i3−2i3−2i32i300000002i2−2i2000000000000−666−6−i2i2i2−i200000000000000000000000
χ704-444-4-44-440000-4-44-44-440000000000000000000000000000000000000000000004i−4i00000000000000000
χ714-444-4-44-440000-4-44-44-44000000000000000000000000000000000000000000000−4i4i00000000000000000
χ724-44-444-4-4-24-4-442-2-2-2222004i−4i4i−4i2-20000-2200000000000−2i2i−2i2i00000000000000000000000000000000000
χ734-44-444-4-4-24-4-442-2-2-222200−4i4i−4i4i2-20000-22000000000002i−2i2i−2i00000000000000000000000000000000000
χ744-44-444-4-4-2-444-42-2-2-2222000000-2200002-204i−4i000000000000−2i2i−2i2i0000000000000000000000000000000
χ754-44-444-4-4-2-444-42-2-2-2222000000-2200002-20−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000
χ764-4-44-44-4440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000022−22000
χ774-4-44-44-4440000-4-4-4444-400000000000000000000000000000000000000000000000000000000000−2222000
χ784-4-4-44-44444-44-4-44-4-4-444000000440000-4-400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-44-42-2222-2-2000000-2-200002200000000000000023−23−23230000000000000000000000000000000
χ804-4-4-44-444-24-44-42-2222-2-2000000-2-2000022000000000000000−232323−230000000000000000000000000000000
χ814-4-4-44-444-2-44-442-2222-2-2004-4-44220000-2-200000000000-222-200000000000000000000000000000000000
χ824-4-4-44-444-2-44-442-2222-2-200-444-4220000-2-2000000000002-2-2200000000000000000000000000000000000
χ838-888-8-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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