Finite Group Databasebeta

← Group #10844648

Character table — Group #10844648

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122244488881212121212121212121224242424242424244444444661212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-11-1-111-1-1-1-1111
χ6111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-1-1-111-1-11111-1-1-1
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1111-1-1111111-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-111-111-1-1-1-1-1-1111
χ911111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
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
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-111-1-1-1-1-11111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11-1-111111-1-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-111-1-1-111-1-111-1-11
χ17222222222-2-2-2-222222220000222222-2-2-2-200-2000000-2-200000000000000002222-2-200000-200000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-200-2000000-2-20000000000000000-2-2-2-22200000200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200200000022000000000000000022-2-22200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000220000000000000000-2-222-2-200000200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-122-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
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
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-2-22-2-222-2-222-2-2-22-2222-2-20000002-2-220000000000022-2-200000000000000000000000000002i−2i2i−2i000
χ30222-2-22-2-222-2-222-2-2-22-2222-2-20000002-2-220000000000022-2-20000000000000000000000000000−2i2i−2i2i000
χ31222-2-22-2-222-2-222-2-2-22-22-2-2220000002-2-2200000000000-2-22200000000000000000000000000002i−2i−2i2i000
χ32222-2-22-2-222-2-222-2-2-22-22-2-2220000002-2-2200000000000-2-2220000000000000000000000000000−2i2i2i−2i000
χ332-2-22-222-222-22-2-2-222-2-222i−2i2i−2i00000022-2-22-20002i−2i00002i−2i2i−2i00002i2i−2i−2i000000000002-200000000000000
χ342-2-22-222-222-22-2-2-222-2-222i−2i2i−2i00000022-2-2-22000−2i2i00002i−2i2i−2i0000−2i−2i2i2i00000000000-2200000000000000
χ352-2-22-222-222-22-2-2-222-2-22−2i2i−2i2i00000022-2-22-2000−2i2i0000−2i2i−2i2i0000−2i−2i2i2i000000000002-200000000000000
χ362-2-22-222-222-22-2-2-222-2-22−2i2i−2i2i00000022-2-2-220002i−2i0000−2i2i−2i2i00002i2i−2i−2i00000000000-2200000000000000
χ372-2-22-222-2-12-22-211-1-111-12i−2i2i−2i00−i3−i3i3i3-1-1112-20002i−2i00−i3i3−ii−ii33−3−3−i−iii33−3−30000000-11−i3i3000000000000
χ382-2-22-222-2-12-22-211-1-111-12i−2i2i−2i00−i3−i3i3i3-1-111-22000−2i2i00−i3i3−ii−ii33−3−3ii−i−i−3−33300000001-1i3−i3000000000000
χ392-2-22-222-2-12-22-211-1-111-12i−2i2i−2i00i3i3−i3−i3-1-1112-20002i−2i00i3−i3−ii−ii−3−333−i−iii−3−3330000000-11i3−i3000000000000
χ402-2-22-222-2-12-22-211-1-111-12i−2i2i−2i00i3i3−i3−i3-1-111-22000−2i2i00i3−i3−ii−ii−3−333ii−i−i33−3−300000001-1−i3i3000000000000
χ412-2-22-222-2-12-22-211-1-111-1−2i2i−2i2i00−i3−i3i3i3-1-1112-2000−2i2i00−i3i3i−ii−i−3−333ii−i−i−3−3330000000-11−i3i3000000000000
χ422-2-22-222-2-12-22-211-1-111-1−2i2i−2i2i00−i3−i3i3i3-1-111-220002i−2i00−i3i3i−ii−i−3−333−i−iii33−3−300000001-1i3−i3000000000000
χ432-2-22-222-2-12-22-211-1-111-1−2i2i−2i2i00i3i3−i3−i3-1-1112-2000−2i2i00i3−i3i−ii−i33−3−3ii−i−i33−3−30000000-11i3−i3000000000000
χ442-2-22-222-2-12-22-211-1-111-1−2i2i−2i2i00i3i3−i3−i3-1-111-220002i−2i00i3−i3i−ii−i33−3−3−i−iii−3−33300000001-1−i3i3000000000000
χ452-2-2-222-22222-2-2-22-2-2-2222i−2i−2i2i0000002-22-2000000000002i−2i−2i2i000000000000002-22-20000002i−2i000000000
χ462-2-2-222-22222-2-2-22-2-2-2222i−2i−2i2i0000002-22-2000000000002i−2i−2i2i00000000000000-22-22000000−2i2i000000000
χ472-2-2-222-22222-2-2-22-2-2-222−2i2i2i−2i0000002-22-200000000000−2i2i2i−2i000000000000002-22-2000000−2i2i000000000
χ482-2-2-222-22222-2-2-22-2-2-222−2i2i2i−2i0000002-22-200000000000−2i2i2i−2i00000000000000-22-220000002i−2i000000000
χ492-2-2-222-222-2-222-22-2-2-2220000000000-22-220002-200000000002-22-200000000002-2-22000000002-20000000
χ502-2-2-222-222-2-222-22-2-2-2220000000000-22-220002-200000000002-22-20000000000-222-200000000-220000000
χ512-2-2-222-222-2-222-22-2-2-2220000000000-22-22000-220000000000-22-2200000000002-2-2200000000-220000000
χ522-2-2-222-222-2-222-22-2-2-2220000000000-22-22000-220000000000-22-220000000000-222-2000000002-20000000
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
χ55444-4-44-4-44-444-44-4-4-44-440000000000-444-400000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-24-4-44-2222-22-244-4-4000000-222-200000000000-2-22200000000000000000000000000000000000
χ57444-4-44-4-4-24-4-44-2222-22-2-4-444000000-222-20000000000022-2-200000000000000000000000000000000000
χ58444-4-44-4-4-2-444-4-2222-22-200000000002-2-2200000000000000023−23−23230000000000000000000000000000000
χ59444-4-44-4-4-2-444-4-2222-22-200000000002-2-22000000000000000−232323−230000000000000000000000000000000
χ6044-444-4-4-4400004-44-4-44-400000000000000000000022−220000000000000022−2222−2200000000000000000000000
χ6144-444-4-4-4400004-44-4-44-4000000000000000000000−222200000000000000−2222−222200000000000000000000000
χ6244-444-4-4-4-20000-22-222-2200000023−2323−230000000000022−2200000000006−66−6−22−2200000000000000000000000
χ6344-444-4-4-4-20000-22-222-2200000023−2323−2300000000000−22220000000000−66−662−22−200000000000000000000000
χ6444-444-4-4-4-20000-22-222-22000000−2323−23230000000000022−220000000000−66−66−22−2200000000000000000000000
χ6544-444-4-4-4-20000-22-222-22000000−2323−232300000000000−222200000000006−66−62−22−200000000000000000000000
χ6644-4-4-4-4444000044-44-4-4-4000000000000000000000000000000000000000004i−4i000000000000000000000
χ6744-4-4-4-4444000044-44-4-4-400000000000000000000000000000000000000000−4i4i000000000000000000000
χ684-444-4-4-4440000-444-44-4-400004i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ694-444-4-4-4440000-444-44-4-40000−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ704-444-4-4-44-200002-2-22-22200004i−4i−2i2i2i−2i00000000000000000000000i6−i6−i6i66−6−6600000000000000000000000
χ714-444-4-4-44-200002-2-22-22200004i−4i−2i2i2i−2i00000000000000000000000−i6i6i6−i6−666−600000000000000000000000
χ724-444-4-4-44-200002-2-22-2220000−4i4i2i−2i−2i2i00000000000000000000000i6−i6−i6i6−666−600000000000000000000000
χ734-444-4-4-44-200002-2-22-2220000−4i4i2i−2i−2i2i00000000000000000000000−i6i6i6−i66−6−6600000000000000000000000
χ744-44-44-44-440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ754-44-44-44-440000-4-4-4444-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ764-4-44-444-44-44-44-4-444-4-440000000000-4-44400000000000000000000000000000000000000000000000000
χ774-4-44-444-4-2-44-4422-2-222-2000000−2i3−2i32i32i322-2-20000000002i3−2i3000000000000000000000000000000000000000
χ784-4-44-444-4-2-44-4422-2-222-20000002i32i3−2i3−2i322-2-2000000000−2i32i3000000000000000000000000000000000000000
χ794-4-4-444-44-244-4-42-2222-2-24i−4i−4i4i000000-22-2200000000000−2i2i2i−2i00000000000000000000000000000000000
χ804-4-4-444-44-244-4-42-2222-2-2−4i4i4i−4i000000-22-22000000000002i−2i−2i2i00000000000000000000000000000000000
χ814-4-4-444-44-2-4-4442-2222-2-200000000002-22-20004-40000000000-22-220000000000000000000000000000000
χ824-4-4-444-44-2-4-4442-2222-2-200000000002-22-2000-4400000000002-22-20000000000000000000000000000000
χ8388-8-8-8-888-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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