Finite Group Databasebeta

← Group #10858985

Character table — Group #10858985

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666444444121212121212121222444666688881212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-1111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-111-1-1-1-1-11111-1-111-1
χ6111111111111111111111111-1-1111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-111-1-11
χ7111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-11-1-111-1-1-111-1-111-1-11
χ8111111111111111111111111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-111111-1-111-1-111-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-111111-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-111111-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-11-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111-111-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-1111111-1-1-1
χ17222222222-2-2-2-22222222000022-2-2-22222-20000-200000000-2-200000000000022-2-22200000-200000000000
χ18222222222-2-2-2-22222222000022-2-2-22222-20000-200000000-2-2000000000000-2-222-2-200000200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200002000000002200000000000022-2-2-2-200000200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000022000000000000-2-2222200000-200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-222-2111122-2-211-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-2-2-21111-2-22211-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-12222-2-1-1-1-1-2-2221111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122-2-2-2-1-1-1-122-2-2111111-1-1-1-11111000000211-1-1000000000000
χ29222-22-2-2-2222-2-2222-2-2-2-200000022-20000-22-200022-2-20000000000000000002-22-2000000002-2000000000
χ30222-22-2-2-2222-2-2222-2-2-2-200000022-20000-22-200022-2-2000000000000000000-22-2200000000-22000000000
χ31222-22-2-2-2222-2-2222-2-2-2-200000022-20000-2-22000-2-2220000000000000000002-22-200000000-22000000000
χ32222-22-2-2-2222-2-2222-2-2-2-200000022-20000-2-22000-2-222000000000000000000-22-22000000002-2000000000
χ33222-22-2-2-22-2-222222-2-2-2-22i2i−2i−2i00-2-22000020000000000000002i2i−2i−2i000000002-2-2200000000002i−2i0000000
χ34222-22-2-2-22-2-222222-2-2-2-22i2i−2i−2i00-2-22000020000000000000002i2i−2i−2i00000000-222-20000000000−2i2i0000000
χ35222-22-2-2-22-2-222222-2-2-2-2−2i−2i2i2i00-2-2200002000000000000000−2i−2i2i2i000000002-2-220000000000−2i2i0000000
χ36222-22-2-2-22-2-222222-2-2-2-2−2i−2i2i2i00-2-2200002000000000000000−2i−2i2i2i00000000-222-200000000002i−2i0000000
χ372-222-2-2-2222-22-2-2-22-222-22i−2i2i−2i002-220000-20000000000000002i−2i2i−2i0000000000000000000000002-2002i−2i0
χ382-222-2-2-2222-22-2-2-22-222-22i−2i2i−2i002-220000-20000000000000002i−2i2i−2i000000000000000000000000-2200−2i2i0
χ392-222-2-2-2222-22-2-2-22-222-2−2i2i−2i2i002-220000-2000000000000000−2i2i−2i2i0000000000000000000000002-200−2i2i0
χ402-222-2-2-2222-22-2-2-22-222-2−2i2i−2i2i002-220000-2000000000000000−2i2i−2i2i000000000000000000000000-22002i−2i0
χ412-22-2-222-22-222-2-2-222-2-222-2-2200-2220000-2002i−2i000002i−2i00002-2-222i2i−2i−2i000000000002i−2i00000000000000
χ422-22-2-222-22-222-2-2-222-2-222-2-2200-2220000-200−2i2i00000−2i2i00002-2-22−2i−2i2i2i00000000000−2i2i00000000000000
χ432-22-2-222-22-222-2-2-222-2-22-222-200-2220000-2002i−2i00000−2i2i0000-222-2−2i−2i2i2i000000000002i−2i00000000000000
χ442-22-2-222-22-222-2-2-222-2-22-222-200-2220000-200−2i2i000002i−2i0000-222-22i2i−2i−2i00000000000−2i2i00000000000000
χ452-22-2-222-2-1-222-211-1-111-12-2-22001-1-1−i3−i3i3i31002i−2i0−i3i3−i3i32i−2i00−i3i3-111-1−i−iii33−3−30000000−ii3−3000000000000
χ462-22-2-222-2-1-222-211-1-111-12-2-22001-1-1−i3−i3i3i3100−2i2i0−i3i3−i3i3−2i2i00−i3i3-111-1ii−i−i−3−3330000000i−i−33000000000000
χ472-22-2-222-2-1-222-211-1-111-12-2-22001-1-1i3i3−i3−i31002i−2i0i3−i3i3−i32i−2i00i3−i3-111-1−i−iii−3−3330000000−ii−33000000000000
χ482-22-2-222-2-1-222-211-1-111-12-2-22001-1-1i3i3−i3−i3100−2i2i0i3−i3i3−i3−2i2i00i3−i3-111-1ii−i−i33−3−30000000i−i3−3000000000000
χ492-22-2-222-2-1-222-211-1-111-1-222-2001-1-1−i3−i3i3i31002i−2i0i3−i3i3−i3−2i2i00−i3i31-1-11ii−i−i−3−3330000000−ii3−3000000000000
χ502-22-2-222-2-1-222-211-1-111-1-222-2001-1-1−i3−i3i3i3100−2i2i0i3−i3i3−i32i−2i00−i3i31-1-11−i−iii33−3−30000000i−i−33000000000000
χ512-22-2-222-2-1-222-211-1-111-1-222-2001-1-1i3i3−i3−i31002i−2i0−i3i3−i3i3−2i2i00i3−i31-1-11ii−i−i33−3−30000000−ii−33000000000000
χ522-22-2-222-2-1-222-211-1-111-1-222-2001-1-1i3i3−i3−i3100−2i2i0−i3i3−i3i32i−2i00i3−i31-1-11−i−iii−3−3330000000i−i3−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044222-2-2-2-220000-4000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222220000400000000-2-200000000000000000000000000000000000
χ55444-44-4-4-4-244-4-4-2-2-22222000000-2-22000024-4000-2-22200000000000000000000000000000000000000000
χ56444-44-4-4-4-244-4-4-2-2-22222000000-2-2200002-4400022-2-200000000000000000000000000000000000000000
χ57444-44-4-4-4-2-4-444-2-2-222224i4i−4i−4i0022-20000-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ58444-44-4-4-4-2-4-444-2-2-22222−4i−4i4i4i0022-20000-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ5944-44-4-44-4400004-4-4-44-4400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ6044-44-4-44-4400004-4-4-44-44000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ6144-4-4-44-44400004-4-44-44-40000000000000000000000000−2i22i20000000000−2i22i2−2i22i200000000000000000000000
χ6244-4-4-44-44400004-4-44-44-400000000000000000000000002i2−2i200000000002i2−2i22i2−2i200000000000000000000000
χ6344-4-4-44-44-20000-222-22-2200000000023−2323−23000000000000−2i22i2000000i6−i6i6−i6i2−i2i2−i200000000000000000000000
χ6444-4-4-44-44-20000-222-22-2200000000023−2323−230000000000002i2−2i2000000−i6i6−i6i6−i2i2−i2i200000000000000000000000
χ6544-4-4-44-44-20000-222-22-22000000000−2323−2323000000000000−2i22i2000000−i6i6−i6i6i2−i2i2−i200000000000000000000000
χ6644-4-4-44-44-20000-222-22-22000000000−2323−23230000000000002i2−2i2000000i6−i6i6−i6−i2i2−i2i200000000000000000000000
χ674-444-4-4-444-44-44-4-44-444-4000000-44-40000400000000000000000000000000000000000000000000000000
χ684-444-4-4-44-24-44-422-22-2-224i−4i4i−4i00-22-200002000000000000000−2i2i−2i2i0000000000000000000000000000000
χ694-444-4-4-44-24-44-422-22-2-22−4i4i−4i4i00-22-2000020000000000000002i−2i2i−2i0000000000000000000000000000000
χ704-444-4-4-44-2-44-4422-22-2-220000002-220000-200000−2i32i32i3−2i300000000000000000000000000000000000000000
χ714-444-4-4-44-2-44-4422-22-2-220000002-220000-2000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ724-44-4-444-444-4-44-4-444-4-440000004-4-40000400000000000000000000000000000000000000000000000000
χ734-44-4-444-4-24-4-4422-2-222-2000000-222−2i3−2i32i32i3-200000000000002i3−2i300000000000000000000000000000000000
χ744-44-4-444-4-24-4-4422-2-222-2000000-2222i32i3−2i3−2i3-20000000000000−2i32i300000000000000000000000000000000000
χ754-4-4444-4-440000-44-444-4-400004i−4i0004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ764-4-4444-4-440000-44-444-4-40000−4i4i000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ774-4-4444-4-4-200002-22-2-22200004i−4i000−2i2i2i−2i000000000000000000006−6−66i6−i6−i6i600000000000000000000000
χ784-4-4444-4-4-200002-22-2-22200004i−4i000−2i2i2i−2i00000000000000000000−666−6−i6i6i6−i600000000000000000000000
χ794-4-4444-4-4-200002-22-2-2220000−4i4i0002i−2i−2i2i000000000000000000006−6−66−i6i6i6−i600000000000000000000000
χ804-4-4444-4-4-200002-22-2-2220000−4i4i0002i−2i−2i2i00000000000000000000−666−6i6−i6−i6i600000000000000000000000
χ814-4-4-44-44440000-44-4-4-4440000000000000000000000000000000000000000000004-400000000000000000
χ824-4-4-44-44440000-44-4-4-444000000000000000000000000000000000000000000000-4400000000000000000
χ8388-88-8-88-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-88-888-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000

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