Finite Group Databasebeta

← Group #10840257

Character table — Group #10840257

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
χ31111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1
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
χ911111111111111111111-1-1111111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1-1-1111
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1-1-1111111-1-1-1
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-111111-1-111-1-1-1
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-1-111-1-1111
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-11111-1-11
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-11111-1-1-1-111-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-11-1-11111-1-111-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-1-111-1-1-1-111-1-11
χ17222222222-2-2-2-22222222220000-2-22222-2-2-20000-2-20000000000000000000022-2-22200000-200000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-20000-2-200000000000000000000-2-222-2-200000200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-22000022000000000000000000002222-2-200000-200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200002200000000000000000000-2-2-2-22200000200000000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-1-1-2-2-2-211111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2221122-2-2-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-211-2-222-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2222211-2-2221111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-21122-2-21111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-2-22-2-2222-22-22-2-22-2-22002i2i−2i−2i220000-2-20002-2002i−2i002i2i−2i−2i00002i2i−2i−2i00000000000002-2000000000000
χ3022-2-22-2-2222-22-22-2-22-2-22002i2i−2i−2i220000-2-2000-2200−2i2i002i2i−2i−2i0000−2i−2i2i2i0000000000000-22000000000000
χ3122-2-22-2-2222-22-22-2-22-2-2200−2i−2i2i2i220000-2-20002-200−2i2i00−2i−2i2i2i0000−2i−2i2i2i00000000000002-2000000000000
χ3222-2-22-2-2222-22-22-2-22-2-2200−2i−2i2i2i220000-2-2000-22002i−2i00−2i−2i2i2i00002i2i−2i−2i0000000000000-22000000000000
χ3322-2-22-2-22-12-22-2-111-111-1002i2i−2i−2i-1-1−i3−i3i3i3110002-2−i3i32i−2i00−i−iii33−3−3−i−iii33−3−30000000−i3i3-11000000000000
χ3422-2-22-2-22-12-22-2-111-111-1002i2i−2i−2i-1-1−i3−i3i3i311000-22−i3i3−2i2i00−i−iii33−3−3ii−i−i−3−3330000000i3−i31-1000000000000
χ3522-2-22-2-22-12-22-2-111-111-1002i2i−2i−2i-1-1i3i3−i3−i3110002-2i3−i32i−2i00−i−iii−3−333−i−iii−3−3330000000i3−i3-11000000000000
χ3622-2-22-2-22-12-22-2-111-111-1002i2i−2i−2i-1-1i3i3−i3−i311000-22i3−i3−2i2i00−i−iii−3−333ii−i−i33−3−30000000−i3i31-1000000000000
χ3722-2-22-2-22-12-22-2-111-111-100−2i−2i2i2i-1-1−i3−i3i3i3110002-2−i3i3−2i2i00ii−i−i−3−333ii−i−i−3−3330000000−i3i3-11000000000000
χ3822-2-22-2-22-12-22-2-111-111-100−2i−2i2i2i-1-1−i3−i3i3i311000-22−i3i32i−2i00ii−i−i−3−333−i−iii33−3−30000000i3−i31-1000000000000
χ3922-2-22-2-22-12-22-2-111-111-100−2i−2i2i2i-1-1i3i3−i3−i3110002-2i3−i3−2i2i00ii−i−i33−3−3ii−i−i33−3−30000000i3−i3-11000000000000
χ4022-2-22-2-22-12-22-2-111-111-100−2i−2i2i2i-1-1i3i3−i3−i311000-22i3−i32i−2i00ii−i−i33−3−3−i−iii−3−3330000000−i3i31-1000000000000
χ412-22-222-2-2222-2-2-2-2-2-2222002-22-22-200002-2000000000002-22-2000000000000000000000000002i−2i002i−2i000
χ422-22-222-2-2222-2-2-2-2-2-2222002-22-22-200002-2000000000002-22-200000000000000000000000000−2i2i00−2i2i000
χ432-22-222-2-2222-2-2-2-2-2-222200-22-222-200002-200000000000-22-22000000000000000000000000002i−2i00−2i2i000
χ442-22-222-2-2222-2-2-2-2-2-222200-22-222-200002-200000000000-22-2200000000000000000000000000−2i2i002i−2i000
χ452-2-222-22-222-2-22-222-2-2-22002i−2i−2i2i2-20000-22000000000002i−2i−2i2i000000000000002-22-200000000002i−2i00000
χ462-2-222-22-222-2-22-222-2-2-22002i−2i−2i2i2-20000-22000000000002i−2i−2i2i00000000000000-22-220000000000−2i2i00000
χ472-2-222-22-222-2-22-222-2-2-2200−2i2i2i−2i2-20000-2200000000000−2i2i2i−2i000000000000002-22-20000000000−2i2i00000
χ482-2-222-22-222-2-22-222-2-2-2200−2i2i2i−2i2-20000-2200000000000−2i2i2i−2i00000000000000-22-2200000000002i−2i00000
χ492-2-222-22-22-222-2-222-2-2-22000000-2200002-202i−2i0000000000002i−2i2i−2i00000000002-2-220000002i−2i000000000
χ502-2-222-22-22-222-2-222-2-2-22000000-2200002-202i−2i0000000000002i−2i2i−2i0000000000-222-2000000−2i2i000000000
χ512-2-222-22-22-222-2-222-2-2-22000000-2200002-20−2i2i000000000000−2i2i−2i2i00000000002-2-22000000−2i2i000000000
χ522-2-222-22-22-222-2-222-2-2-22000000-2200002-20−2i2i000000000000−2i2i−2i2i0000000000-222-20000002i−2i000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000220000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222222240000-2-20000000000000000000000000000000000000000000
χ55444-4-4-44-44000044-4-44-4-4000000000000000000000000000000000000000000000000000000000000022−220
χ56444-4-4-44-44000044-4-44-4-40000000000000000000000000000000000000000000000000000000000000−22220
χ5744-44-44-4-4400004-44-4-44-4000000000000000000000000000000000000000004-4000000000000000000000
χ5844-44-44-4-4400004-44-4-44-400000000000000000000000000000000000000000-44000000000000000000000
χ5944-4-44-4-444-44-444-4-44-4-44000000-4-400004400000000000000000000000000000000000000000000000000
χ6044-4-44-4-44-2-44-44-222-222-200000022−2i3−2i32i32i3-2-2000002i3−2i30000000000000000000000000000000000000000000
χ6144-4-44-4-44-2-44-44-222-222-2000000222i32i3−2i3−2i3-2-200000−2i32i30000000000000000000000000000000000000000000
χ624-444-4-4-4440000-4-4444-4-44i−4i0000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ634-444-4-4-4440000-4-4444-4-4−4i4i000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ644-444-4-4-44-2000022-2-2-2224i−4i000000−2i2i−2i2i000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ654-444-4-4-44-2000022-2-2-2224i−4i000000−2i2i−2i2i000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ664-444-4-4-44-2000022-2-2-222−4i4i0000002i−2i2i−2i000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ674-444-4-4-44-2000022-2-2-222−4i4i0000002i−2i2i−2i000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ684-44-444-4-44-4-444-4-4-4-4444000000-440000-4400000000000000000000000000000000000000000000000000
χ694-44-444-4-4-244-4-42222-2-2-2004-44-4-220000-2200000000000-22-2200000000000000000000000000000000000
χ704-44-444-4-4-244-4-42222-2-2-200-44-44-220000-22000000000002-22-200000000000000000000000000000000000
χ714-44-444-4-4-2-4-4442222-2-2-20000002-200002-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ724-44-444-4-4-2-4-4442222-2-2-20000002-200002-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ734-4-444-44-4-24-4-442-2-2222-2004i−4i−4i4i-2200002-200000000000−2i2i2i−2i00000000000000000000000000000000000
χ744-4-444-44-4-24-4-442-2-2222-200−4i4i4i−4i-2200002-2000000000002i−2i−2i2i00000000000000000000000000000000000
χ754-4-444-44-4-2-444-42-2-2222-20000002-20000-2204i−4i000000000000−2i2i−2i2i0000000000000000000000000000000
χ764-4-444-44-4-2-444-42-2-2222-20000002-20000-220−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000
χ774-4-4-4-444440000-44-44-44-40000000000000000000000022−2200000000000022−22−222200000000000000000000000
χ784-4-4-4-444440000-44-44-44-400000000000000000000000−2222000000000000−222222−2200000000000000000000000
χ794-4-4-4-4444-200002-22-22-220000000023−23−23230000000000022−22000000006−6−66−222−200000000000000000000000
χ804-4-4-4-4444-200002-22-22-220000000023−23−232300000000000−222200000000−666−62−2−2200000000000000000000000
χ814-4-4-4-4444-200002-22-22-2200000000−232323−230000000000022−2200000000−666−6−222−200000000000000000000000
χ824-4-4-4-4444-200002-22-22-2200000000−232323−2300000000000−2222000000006−6−662−2−2200000000000000000000000
χ83888-8-8-88-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-88-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000

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