Finite Group Databasebeta

← Group #10859065

Character table — Group #10859065

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1111111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-111-1-111-1-1-111-1-111-1
χ1011111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-11111-1-11
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11111111-1-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-1111-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-1111-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-1111-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-22222-200-200000000000000-2-2000000002222-2-2000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-22222-200-200000000000000-2-200000000-2-2-2-22200000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200200000000000000220000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000000000002200000000-2-22222000000000-20000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-211111111-1-1111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-2222211111111-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-22222-2-2-1-1-1-1111111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-222-1-1-1-11111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-222-2-2221111-1-1-1-1111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-222-2-21111-1-1-1-111-1-1-1-11111000000211-1-1000000000000
χ29222-2-2-22-2222-2-22-22-22-2-200000022-20000-22-20000000000022-2-200000000002-2002-200000002-200000000
χ30222-2-2-22-2222-2-22-22-22-2-200000022-20000-22-20000000000022-2-20000000000-2200-220000000-2200000000
χ31222-2-2-22-2222-2-22-22-22-2-200000022-20000-2-2200000000000-2-22200000000002-2002-20000000-2200000000
χ32222-2-2-22-2222-2-22-22-22-2-200000022-20000-2-2200000000000-2-2220000000000-2200-2200000002-200000000
χ33222-2-2-22-22-2-2222-22-22-2-2002i2i−2i−2i-2-22000020000000002i2i−2i−2i000000000000002-200-2200000000002i−2i00000
χ34222-2-2-22-22-2-2222-22-22-2-2002i2i−2i−2i-2-22000020000000002i2i−2i−2i00000000000000-22002-20000000000−2i2i00000
χ35222-2-2-22-22-2-2222-22-22-2-200−2i−2i2i2i-2-2200002000000000−2i−2i2i2i000000000000002-200-220000000000−2i2i00000
χ36222-2-2-22-22-2-2222-22-22-2-200−2i−2i2i2i-2-2200002000000000−2i−2i2i2i00000000000000-22002-200000000002i−2i00000
χ372-2-222-22-222-22-2-2-222-2-22002i−2i2i−2i2-220000-20002-22i−2i002i−2i2i−2i0000002i2i−2i−2i000000000002-200000000000000
χ382-2-222-22-222-22-2-2-222-2-22002i−2i2i−2i2-220000-2000-22−2i2i002i−2i2i−2i000000−2i−2i2i2i00000000000-2200000000000000
χ392-2-222-22-222-22-2-2-222-2-2200−2i2i−2i2i2-220000-20002-2−2i2i00−2i2i−2i2i000000−2i−2i2i2i000000000002-200000000000000
χ402-2-222-22-222-22-2-2-222-2-2200−2i2i−2i2i2-220000-2000-222i−2i00−2i2i−2i2i0000002i2i−2i−2i00000000000-2200000000000000
χ412-2-222-22-2-12-22-211-1-111-1002i−2i2i−2i-11-1−i3−i3i3i310002-22i−2i00−ii−ii3−33−3−i3i3−i−iii33−3−30000000-11−i3i3000000000000
χ422-2-222-22-2-12-22-211-1-111-1002i−2i2i−2i-11-1−i3−i3i3i31000-22−2i2i00−ii−ii3−33−3−i3i3ii−i−i−3−33300000001-1i3−i3000000000000
χ432-2-222-22-2-12-22-211-1-111-1002i−2i2i−2i-11-1i3i3−i3−i310002-22i−2i00−ii−ii−33−33i3−i3−i−iii−3−3330000000-11i3−i3000000000000
χ442-2-222-22-2-12-22-211-1-111-1002i−2i2i−2i-11-1i3i3−i3−i31000-22−2i2i00−ii−ii−33−33i3−i3ii−i−i33−3−300000001-1−i3i3000000000000
χ452-2-222-22-2-12-22-211-1-111-100−2i2i−2i2i-11-1−i3−i3i3i310002-2−2i2i00i−ii−i−33−33−i3i3ii−i−i−3−3330000000-11−i3i3000000000000
χ462-2-222-22-2-12-22-211-1-111-100−2i2i−2i2i-11-1−i3−i3i3i31000-222i−2i00i−ii−i−33−33−i3i3−i−iii33−3−300000001-1i3−i3000000000000
χ472-2-222-22-2-12-22-211-1-111-100−2i2i−2i2i-11-1i3i3−i3−i310002-2−2i2i00i−ii−i3−33−3i3−i3ii−i−i33−3−30000000-11i3−i3000000000000
χ482-2-222-22-2-12-22-211-1-111-100−2i2i−2i2i-11-1i3i3−i3−i31000-222i−2i00i−ii−i3−33−3i3−i3−i−iii−3−33300000001-1−i3i3000000000000
χ492-2-2-2-22222-222-2-222-2-22-2002-2-22-2220000-20000000002-2-2200000000000000000000000002i−2i00000002i−2i0
χ502-2-2-2-22222-222-2-222-2-22-2002-2-22-2220000-20000000002-2-220000000000000000000000000−2i2i0000000−2i2i0
χ512-2-2-2-22222-222-2-222-2-22-200-222-2-2220000-2000000000-222-200000000000000000000000002i−2i0000000−2i2i0
χ522-2-2-2-22222-222-2-222-2-22-200-222-2-2220000-2000000000-222-20000000000000000000000000−2i2i00000002i−2i0
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-2200-400000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222222200400000000000000-2-20000000000000000000000000000000
χ55444-4-4-44-4-244-4-4-22-22-222000000-2-22000024-400000000000-2-222000000000000000000000000000000000
χ56444-4-4-44-4-244-4-4-22-22-222000000-2-2200002-440000000000022-2-2000000000000000000000000000000000
χ57444-4-4-44-4-2-4-444-22-22-222004i4i−4i−4i22-20000-2000000000−2i−2i2i2i0000000000000000000000000000000000000
χ58444-4-4-44-4-2-4-444-22-22-22200−4i−4i4i4i22-20000-20000000002i2i−2i−2i0000000000000000000000000000000000000
χ5944-44-4-4-44400004-4-4-4-44400000000000000000000000000000000000000000004i−4i0000000000000000000
χ6044-44-4-4-44400004-4-4-4-4440000000000000000000000000000000000000000000−4i4i0000000000000000000
χ6144-4-444-4-44000044-44-4-4-44-400000004-44-4000000000000000000000000000000000000000000000000000
χ6244-4-444-4-44000044-44-4-4-4-440000000-44-44000000000000000000000000000000000000000000000000000
χ6344-4-444-4-4-20000-2-22-22224-40000000-22-2200000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ6444-4-444-4-4-20000-2-22-22224-40000000-22-2200000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ6544-4-444-4-4-20000-2-22-2222-4400000002-22-200000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ6644-4-444-4-4-20000-2-22-2222-4400000002-22-200000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ674-444-44-4-440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ684-444-44-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ694-44-44-4-4440000-4-4-4444-4000000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000000
χ704-44-44-4-4440000-4-4-4444-40000000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000
χ714-44-44-4-44-20000222-2-2-22000000000−2i32i32i3−2i300000000−2i22i20000000000−666−6i2−i2−i2i200000000000000000000000
χ724-44-44-4-44-20000222-2-2-22000000000−2i32i32i3−2i3000000002i2−2i200000000006−6−66−i2i2i2−i200000000000000000000000
χ734-44-44-4-44-20000222-2-2-220000000002i3−2i3−2i32i300000000−2i22i200000000006−6−66i2−i2−i2i200000000000000000000000
χ744-44-44-4-44-20000222-2-2-220000000002i3−2i3−2i32i3000000002i2−2i20000000000−666−6−i2i2i2−i200000000000000000000000
χ754-4-444-44-44-44-44-4-444-4-44000000-44-40000400000000000000000000000000000000000000000000000000
χ764-4-444-44-4-2-44-4422-2-222-20000002-22−2i3−2i32i32i3-2000000000000000002i3−2i30000000000000000000000000000000
χ774-4-444-44-4-2-44-4422-2-222-20000002-222i32i3−2i3−2i3-200000000000000000−2i32i30000000000000000000000000000000
χ784-4-4-4-444444-4-44-444-4-44-40000004-4-40000400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-4-442-2-222-22000000-2220000-2000000000000023−23−2323000000000000000000000000000000000
χ804-4-4-4-4444-24-4-442-2-222-22000000-2220000-20000000000000−232323−23000000000000000000000000000000000
χ814-4-4-4-4444-2-444-42-2-222-22004-4-442-2-200002000000000-222-20000000000000000000000000000000000000
χ824-4-4-4-4444-2-444-42-2-222-2200-444-42-2-2000020000000002-2-220000000000000000000000000000000000000
χ8388-88-8-8-88-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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