Finite Group Databasebeta

← Group #10844665

Character table — Group #10844665

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212444444488884
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
χ5111111111111111111111111-1-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-111-1-11111-1-1-1
χ6111111111111111111111111-1-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11-1-111-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-111-111-1-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-1111-1-1111111-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-1-11111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1111-1-1-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-111111-1-111-1-111-1
χ17222222222-2-2-2-222222220000222222-2-2-2-200-2000000-2-2000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-200-2000000-2-20000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-20020000002200000000000000002222-2-200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000220000000000000000-2-2-2-22200000200000000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-22222-2-211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-222-2-222111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-2-2-2-2222-2-222-2-22-2-2222-2-20000002-22-20002i−2i2i−2i000022-2-200002i2i−2i−2i000000000002i−2i00000000000000
χ30222-2-2-2-2222-2-222-2-22-2-2222-2-20000002-22-2000−2i2i−2i2i000022-2-20000−2i−2i2i2i00000000000−2i2i00000000000000
χ31222-2-2-2-2222-2-222-2-22-2-22-2-2220000002-22-20002i−2i−2i2i0000-2-2220000−2i−2i2i2i000000000002i−2i00000000000000
χ32222-2-2-2-2222-2-222-2-22-2-22-2-2220000002-22-2000−2i2i2i−2i0000-2-22200002i2i−2i−2i00000000000−2i2i00000000000000
χ33222-2-2-2-22-12-2-22-111-111-122-2-20033−3−3-11-110002i−2i2i−2i003−3-1-11133−3−3−i−iii−i3−i3i3i30000000−ii−i3i3000000000000
χ34222-2-2-2-22-12-2-22-111-111-122-2-20033−3−3-11-11000−2i2i−2i2i003−3-1-11133−3−3ii−i−ii3i3−i3−i30000000i−ii3−i3000000000000
χ35222-2-2-2-22-12-2-22-111-111-122-2-200−3−333-11-110002i−2i2i−2i00−33-1-111−3−333−i−iiii3i3−i3−i30000000−iii3−i3000000000000
χ36222-2-2-2-22-12-2-22-111-111-122-2-200−3−333-11-11000−2i2i−2i2i00−33-1-111−3−333ii−i−i−i3−i3i3i30000000i−i−i3i3000000000000
χ37222-2-2-2-22-12-2-22-111-111-1-2-2220033−3−3-11-110002i−2i−2i2i003−311-1-1−3−333ii−i−ii3i3−i3−i30000000−ii−i3i3000000000000
χ38222-2-2-2-22-12-2-22-111-111-1-2-2220033−3−3-11-11000−2i2i2i−2i003−311-1-1−3−333−i−iii−i3−i3i3i30000000i−ii3−i3000000000000
χ39222-2-2-2-22-12-2-22-111-111-1-2-22200−3−333-11-110002i−2i−2i2i00−3311-1-133−3−3ii−i−i−i3−i3i3i30000000−iii3−i3000000000000
χ40222-2-2-2-22-12-2-22-111-111-1-2-22200−3−333-11-11000−2i2i2i−2i00−3311-1-133−3−3−i−iiii3i3−i3−i30000000i−i−i3i3000000000000
χ412-2-22-22-2222-22-2-222-2-2-222i−2i2i−2i0000002-2-22000000000002i−2i2i−2i00000000000000000000000000002-22i−2i000
χ422-2-22-22-2222-22-2-222-2-2-222i−2i2i−2i0000002-2-22000000000002i−2i2i−2i0000000000000000000000000000-22−2i2i000
χ432-2-22-22-2222-22-2-222-2-2-22−2i2i−2i2i0000002-2-2200000000000−2i2i−2i2i00000000000000000000000000002-2−2i2i000
χ442-2-22-22-2222-22-2-222-2-2-22−2i2i−2i2i0000002-2-2200000000000−2i2i−2i2i0000000000000000000000000000-222i−2i000
χ452-2-2-22-222222-2-2-2-2-2-22222i−2i−2i2i00000022-2-2000000000002i−2i−2i2i0000000000002-2002-20000002i−2i000000000
χ462-2-2-22-222222-2-2-2-2-2-22222i−2i−2i2i00000022-2-2000000000002i−2i−2i2i000000000000-2200-22000000−2i2i000000000
χ472-2-2-22-222222-2-2-2-2-2-2222−2i2i2i−2i00000022-2-200000000000−2i2i2i−2i0000000000002-2002-2000000−2i2i000000000
χ482-2-2-22-222222-2-2-2-2-2-2222−2i2i2i−2i00000022-2-200000000000−2i2i2i−2i000000000000-2200-220000002i−2i000000000
χ492-2-2-22-2222-2-222-2-2-2-22220000000000-2-2222-200000000000002-22-2000000002-200-22000000002-20000000
χ502-2-2-22-2222-2-222-2-2-2-22220000000000-2-2222-200000000000002-22-200000000-22002-200000000-220000000
χ512-2-2-22-2222-2-222-2-2-2-22220000000000-2-222-220000000000000-22-22000000002-200-2200000000-220000000
χ522-2-2-22-2222-2-222-2-2-2-22220000000000-2-222-220000000000000-22-2200000000-22002-2000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-2222200-400000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-422222222004000000-2-2000000000000000000000000000000000000000
χ55444-4-4-4-444-444-44-4-44-4-440000000000-44-4400000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-2-444-4-222-222-20000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ57444-4-4-4-44-2-444-4-222-222-2000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ5844-44-4-44-44000044-4-44-4-4000000000000000000000000000000000000000000000000000000000000022−220
χ5944-44-4-44-44000044-4-44-4-40000000000000000000000000000000000000000000000000000000000000−22220
χ6044-4-444-4-4400004-44-4-44-400000000000000000000000000000000000000000004-40000000000000000000
χ6144-4-444-4-4400004-44-4-44-40000000000000000000000000000000000000000000-440000000000000000000
χ624-4444-4-4-440000-44-44-44-400004-44-44-4000000000000000000000000000000000000000000000000000000
χ634-4444-4-4-440000-44-44-44-40000-44-44-44000000000000000000000000000000000000000000000000000000
χ644-4444-4-4-4-200002-22-22-2200004-4-22-22000000000000000000000006−66−66−66−600000000000000000000000
χ654-4444-4-4-4-200002-22-22-2200004-4-22-2200000000000000000000000−66−66−66−6600000000000000000000000
χ664-4444-4-4-4-200002-22-22-220000-442-22-2000000000000000000000006−66−6−66−6600000000000000000000000
χ674-4444-4-4-4-200002-22-22-220000-442-22-200000000000000000000000−66−666−66−600000000000000000000000
χ684-44-4-444-440000-4-4444-4-4000000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000000
χ694-44-4-444-440000-4-4444-4-40000000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000
χ704-44-4-444-4-2000022-2-2-22200000023−23−232300000000000−2i22i20000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ714-44-4-444-4-2000022-2-2-22200000023−23−2323000000000002i2−2i20000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ724-44-4-444-4-2000022-2-2-222000000−232323−2300000000000−2i22i20000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ734-44-4-444-4-2000022-2-2-222000000−232323−23000000000002i2−2i20000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ744-4-44-44-444-44-44-444-4-4-440000000000-444-400000000000000000000000000000000000000000000000000
χ754-4-44-44-44-24-44-42-2-2222-24i−4i4i−4i000000-222-200000000000−2i2i−2i2i00000000000000000000000000000000000
χ764-4-44-44-44-24-44-42-2-2222-2−4i4i−4i4i000000-222-2000000000002i−2i2i−2i00000000000000000000000000000000000
χ774-4-44-44-44-2-44-442-2-2222-200000000002-2-2200000000000000023−23−23230000000000000000000000000000000
χ784-4-44-44-44-2-44-442-2-2222-200000000002-2-22000000000000000−232323−230000000000000000000000000000000
χ794-4-4-44-444-244-4-42222-2-2-24i−4i−4i4i000000-2-22200000000000−2i2i2i−2i00000000000000000000000000000000000
χ804-4-4-44-444-244-4-42222-2-2-2−4i4i4i−4i000000-2-222000000000002i−2i−2i2i00000000000000000000000000000000000
χ814-4-4-44-444-2-4-4442222-2-2-2000000000022-2-24-40000000000000-22-220000000000000000000000000000000
χ824-4-4-44-444-2-4-4442222-2-2-2000000000022-2-2-4400000000000002-22-20000000000000000000000000000000
χ8388-88-8-88-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000

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