Finite Group Databasebeta

← Group #10844670

Character table — Group #10844670

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212124444488881212121212121212121224242424242424244444442661212444444488882
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
χ5111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-111-111-1-11111-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1111-1-111-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-111-1-1-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-11-1-1111111-1-1-1
χ911111111111111111111-1-1-1-1111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-1111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-1-1-11111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111111-1-1-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-1-1-1-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-111-1
χ17222222222-2-2-2-222222220000222222-2-2-2-20000-20000-2-2000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-20000-20000-2-20000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-20000200002200000000000000002222-2-200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000220000000000000000-2-2-2-22200000200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-122-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-222-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ292222-2-2-2-222-2-222-2-2-22-2222-2-20000002-2-220000000000022-2-200000000000000000000000000002i−2i2i−2i000
χ302222-2-2-2-222-2-222-2-2-22-2222-2-20000002-2-220000000000022-2-20000000000000000000000000000−2i2i−2i2i000
χ312222-2-2-2-222-2-222-2-2-22-22-2-2220000002-2-2200000000000-2-22200000000000000000000000000002i−2i−2i2i000
χ322222-2-2-2-222-2-222-2-2-22-22-2-2220000002-2-2200000000000-2-2220000000000000000000000000000−2i2i2i−2i000
χ332-2-222-22-222-22-2-2-222-2-222i−2i2i−2i00000022-2-22-20002i−2i00002i−2i2i−2i00002i2i−2i−2i00000000000002-2000000000000
χ342-2-222-22-222-22-2-2-222-2-222i−2i2i−2i00000022-2-2-22000−2i2i00002i−2i2i−2i0000−2i−2i2i2i0000000000000-22000000000000
χ352-2-222-22-222-22-2-2-222-2-22−2i2i−2i2i00000022-2-22-2000−2i2i0000−2i2i−2i2i0000−2i−2i2i2i00000000000002-2000000000000
χ362-2-222-22-222-22-2-2-222-2-22−2i2i−2i2i00000022-2-2-220002i−2i0000−2i2i−2i2i00002i2i−2i−2i0000000000000-22000000000000
χ372-2-222-22-2-12-22-211-1-111-12i−2i2i−2i00−i3−i3i3i3-1-1112-20002i−2i00−i3i3−ii−ii33−3−3−i−iii33−3−30000000−i3i3-11000000000000
χ382-2-222-22-2-12-22-211-1-111-12i−2i2i−2i00−i3−i3i3i3-1-111-22000−2i2i00−i3i3−ii−ii33−3−3ii−i−i−3−3330000000i3−i31-1000000000000
χ392-2-222-22-2-12-22-211-1-111-12i−2i2i−2i00i3i3−i3−i3-1-1112-20002i−2i00i3−i3−ii−ii−3−333−i−iii−3−3330000000i3−i3-11000000000000
χ402-2-222-22-2-12-22-211-1-111-12i−2i2i−2i00i3i3−i3−i3-1-111-22000−2i2i00i3−i3−ii−ii−3−333ii−i−i33−3−30000000−i3i31-1000000000000
χ412-2-222-22-2-12-22-211-1-111-1−2i2i−2i2i00−i3−i3i3i3-1-1112-2000−2i2i00−i3i3i−ii−i−3−333ii−i−i−3−3330000000−i3i3-11000000000000
χ422-2-222-22-2-12-22-211-1-111-1−2i2i−2i2i00−i3−i3i3i3-1-111-220002i−2i00−i3i3i−ii−i−3−333−i−iii33−3−30000000i3−i31-1000000000000
χ432-2-222-22-2-12-22-211-1-111-1−2i2i−2i2i00i3i3−i3−i3-1-1112-2000−2i2i00i3−i3i−ii−i33−3−3ii−i−i33−3−30000000i3−i3-11000000000000
χ442-2-222-22-2-12-22-211-1-111-1−2i2i−2i2i00i3i3−i3−i3-1-111-220002i−2i00i3−i3i−ii−i33−3−3−i−iii−3−3330000000−i3i31-1000000000000
χ452-2-22-22-22222-2-2-22-2-2-2222i−2i−2i2i0000002-22-2000000000002i−2i−2i2i0000000000002-2002-20000002i−2i000000000
χ462-2-22-22-22222-2-2-22-2-2-2222i−2i−2i2i0000002-22-2000000000002i−2i−2i2i000000000000-2200-22000000−2i2i000000000
χ472-2-22-22-22222-2-2-22-2-2-222−2i2i2i−2i0000002-22-200000000000−2i2i2i−2i0000000000002-2002-2000000−2i2i000000000
χ482-2-22-22-22222-2-2-22-2-2-222−2i2i2i−2i0000002-22-200000000000−2i2i2i−2i000000000000-2200-220000002i−2i000000000
χ492-2-22-22-222-2-222-22-2-2-2220000000000-22-22002-2000000000002-22-2000000002-200-22000000002-20000000
χ502-2-22-22-222-2-222-22-2-2-2220000000000-22-22002-2000000000002-22-200000000-22002-200000000-220000000
χ512-2-22-22-222-2-222-22-2-2-2220000000000-22-2200-2200000000000-22-22000000002-200-2200000000-220000000
χ522-2-22-22-222-2-222-22-2-2-2220000000000-22-2200-2200000000000-22-2200000000-22002-2000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-222220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-422222222000040000-2-2000000000000000000000000000000000000000
χ554444-4-4-4-44-444-44-4-4-44-440000000000-444-400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44-2222-22-244-4-4000000-222-200000000000-2-22200000000000000000000000000000000000
χ574444-4-4-4-4-24-4-44-2222-22-2-4-444000000-222-20000000000022-2-200000000000000000000000000000000000
χ584444-4-4-4-4-2-444-4-2222-22-200000000002-2-2200000000000000023−23−23230000000000000000000000000000000
χ594444-4-4-4-4-2-444-4-2222-22-200000000002-2-22000000000000000−232323−230000000000000000000000000000000
χ6044-4-44-4-4440000444-4-4-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ6144-4-44-4-4440000444-4-4-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ6244-4-4-444-4400004-4-44-44-400004i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ6344-4-4-444-4400004-4-44-44-40000−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ6444-4-4-444-4-20000-222-22-2200004i−4i−2i2i−2i2i00000000000000000000000i6−i6i6−i66−66−600000000000000000000000
χ6544-4-4-444-4-20000-222-22-2200004i−4i−2i2i−2i2i00000000000000000000000−i6i6−i6i6−66−6600000000000000000000000
χ6644-4-4-444-4-20000-222-22-220000−4i4i2i−2i2i−2i00000000000000000000000i6−i6i6−i6−66−6600000000000000000000000
χ6744-4-4-444-4-20000-222-22-220000−4i4i2i−2i2i−2i00000000000000000000000−i6i6−i6i66−66−600000000000000000000000
χ684-44-444-4-440000-4-44-444-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ694-44-444-4-440000-4-44-444-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ704-44-4-4-44440000-44-444-4-400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ714-44-4-4-44440000-44-444-4-4000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ724-44-4-4-444-200002-22-2-22200000023−23−23230000000000022−2200000000006−6−66−222−200000000000000000000000
χ734-44-4-4-444-200002-22-2-22200000023−23−232300000000000−22220000000000−666−62−2−2200000000000000000000000
χ744-44-4-4-444-200002-22-2-222000000−232323−230000000000022−220000000000−666−6−222−200000000000000000000000
χ754-44-4-4-444-200002-22-2-222000000−232323−2300000000000−222200000000006−6−662−2−2200000000000000000000000
χ764-4-444-44-44-44-44-4-444-4-440000000000-4-44400000000000000000000000000000000000000000000000000
χ774-4-444-44-4-2-44-4422-2-222-2000000−2i3−2i32i32i322-2-20000000002i3−2i3000000000000000000000000000000000000000
χ784-4-444-44-4-2-44-4422-2-222-20000002i32i3−2i3−2i322-2-2000000000−2i32i3000000000000000000000000000000000000000
χ794-4-44-44-44-244-4-42-2222-2-24i−4i−4i4i000000-22-2200000000000−2i2i2i−2i00000000000000000000000000000000000
χ804-4-44-44-44-244-4-42-2222-2-2−4i4i4i−4i000000-22-22000000000002i−2i−2i2i00000000000000000000000000000000000
χ814-4-44-44-44-2-4-4442-2222-2-200000000002-22-2004-400000000000-22-220000000000000000000000000000000
χ824-4-44-44-44-2-4-4442-2222-2-200000000002-22-200-44000000000002-22-20000000000000000000000000000000
χ8388-8-88-8-88-40000-4-4-444440000000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000

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