Finite Group Databasebeta

← Group #10840219

Character table — Group #10840219

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212121212121616161624242424242424244848
order12222222344446666666444412121212121212122244444466668888121212121212242424242424242422444444121212122444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ41111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ511111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ911111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-111111-1-11-1
χ1011111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-1-1-1-111-11
χ1111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-11-1-1-1-1111-1
χ1211111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111-11111-1-1-11
χ1311111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1111-1-111-11
χ1411111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111111111-1-11-1-1-111-1-11-1
χ1511111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-111-11-1-111-1-1-11
χ1611111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-1111-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000000000000022000000000000222200000000-2-200000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000000000000022000000000000-2-2-2-2000000002200000000
χ19222222222-2-2-2-22222222-2-222-2-2-22222-20000000000000000-2-200000000000022-2-2000000002-200000000
χ20222222222-2-2-2-22222222-2-222-2-2-22222-20000000000000000-2-2000000000000-2-22200000000-2200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000000011110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-2221111-2-2-2-2-1-111111111111100000000-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-12222-2-2-2-2-1-1-1-122-2-2111111-1-1-1-1111100000000-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-122-2-2-2-222-1-1-1-1-2-2221111111111-1-1-1-10000000011-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-22222-2-21111-2-22211-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-2-2-22222111122-2-211-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ2922-2-2-22-2222-22-2222-2-2-2-2000022-20000-22-200000022-2-200000000000000000000002i2i−2i−2i00000000002i−2i00
χ3022-2-2-22-2222-22-2222-2-2-2-2000022-20000-22-200000022-2-20000000000000000000000−2i−2i2i2i0000000000−2i2i00
χ3122-2-2-22-2222-22-2222-2-2-2-2000022-20000-2-22000000-2-22200000000000000000000002i2i−2i−2i0000000000−2i2i00
χ3222-2-2-22-2222-22-2222-2-2-2-2000022-20000-2-22000000-2-2220000000000000000000000−2i−2i2i2i00000000002i−2i00
χ332-22-222-2-2222-2-2-2-222-2-222-22-22-2-222-2-2200000000000000002-200000000000000002i−2i2i−2i0000002i−2i000000
χ342-22-222-2-2222-2-2-2-222-2-222-22-22-2-222-2-2200000000000000002-20000000000000000−2i2i−2i2i000000−2i2i000000
χ352-22-222-2-2222-2-2-2-222-2-22-22-222-2-2-2-22220000000000000000-2200000000000000002i−2i2i−2i000000−2i2i000000
χ362-22-222-2-2222-2-2-2-222-2-22-22-222-2-2-2-22220000000000000000-220000000000000000−2i2i−2i2i0000002i−2i000000
χ372-22-222-2-22-2-222-2-222-2-222-2-22-222-2-222-2002i−2i002i−2i000000002-2000000000000000000002i−2i2i−2i0000000000
χ382-22-222-2-22-2-222-2-222-2-222-2-22-222-2-222-200−2i2i00−2i2i000000002-200000000000000000000−2i2i−2i2i0000000000
χ392-22-222-2-22-2-222-2-222-2-22-222-2-22222-2-2-2002i−2i00−2i2i00000000-22000000000000000000002i−2i−2i2i0000000000
χ402-22-222-2-22-2-222-2-222-2-22-222-2-22222-2-2-200−2i2i002i−2i00000000-2200000000000000000000−2i2i2i−2i0000000000
χ412-22-222-2-2-1-2-22211-1-111-12-2-221-1-111-1-11002i−2i002i−2i−i3i3−i3i30000-11−i3−i3i3i333−3−333−3−300000000−ii−ii0000000000
χ422-22-222-2-2-1-2-22211-1-111-12-2-221-1-111-1-11002i−2i002i−2ii3−i3i3−i30000-11i3i3−i3−i3−3−333−3−33300000000−ii−ii0000000000
χ432-22-222-2-2-1-2-22211-1-111-12-2-221-1-111-1-1100−2i2i00−2i2i−i3i3−i3i30000-11−i3−i3i3i3−3−333−3−33300000000i−ii−i0000000000
χ442-22-222-2-2-1-2-22211-1-111-12-2-221-1-111-1-1100−2i2i00−2i2ii3−i3i3−i30000-11i3i3−i3−i333−3−333−3−300000000i−ii−i0000000000
χ452-22-222-2-2-1-2-22211-1-111-1-222-21-1-1-1-1111002i−2i00−2i2i−i3i3−i3i300001-1i3i3−i3−i333−3−3−3−33300000000−iii−i0000000000
χ462-22-222-2-2-1-2-22211-1-111-1-222-21-1-1-1-1111002i−2i00−2i2ii3−i3i3−i300001-1−i3−i3i3i3−3−33333−3−300000000−iii−i0000000000
χ472-22-222-2-2-1-2-22211-1-111-1-222-21-1-1-1-111100−2i2i002i−2i−i3i3−i3i300001-1i3i3−i3−i3−3−33333−3−300000000i−i−ii0000000000
χ482-22-222-2-2-1-2-22211-1-111-1-222-21-1-1-1-111100−2i2i002i−2ii3−i3i3−i300001-1−i3−i3i3i333−3−3−3−33300000000i−i−ii0000000000
χ492-2-22-222-222-2-22-2-22-222-200002-220000-200002i−2i0000000000002i−2i2i−2i0000000000002-2-22000000002i−2i0000
χ502-2-22-222-222-2-22-2-22-222-200002-220000-200002i−2i0000000000002i−2i2i−2i000000000000-222-200000000−2i2i0000
χ512-2-22-222-222-2-22-2-22-222-200002-220000-20000−2i2i000000000000−2i2i−2i2i0000000000002-2-2200000000−2i2i0000
χ522-2-22-222-222-2-22-2-22-222-200002-220000-20000−2i2i000000000000−2i2i−2i2i000000000000-222-2000000002i−2i0000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222222220000000000000000-2-20000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222-2-2-2-220000000000000000220000000000000000000000000000000000
χ554444-4-4-4-4400004-4-444-4-400000000000000000000000022−220000000022−2222−2200000000000000000000000000
χ564444-4-4-4-4400004-4-444-4-4000000000000000000000000−222200000000−2222−222200000000000000000000000000
χ574444-4-4-4-4-20000-222-2-222000000023−2323−23000000000000022−2200000000−22−226−66−60000000000000000000000
χ584444-4-4-4-4-20000-222-2-222000000023−2323−230000000000000−2222000000002−22−2−66−660000000000000000000000
χ594444-4-4-4-4-20000-222-2-2220000000−2323−2323000000000000022−2200000000−22−22−66−660000000000000000000000
χ604444-4-4-4-4-20000-222-2-2220000000−2323−23230000000000000−2222000000002−22−26−66−60000000000000000000000
χ6144-4-44-44-4400004-4-4-4-444000000000000000000000000000000000000000000004i−4i000000000000000000
χ6244-4-44-44-4400004-4-4-4-44400000000000000000000000000000000000000000000−4i4i000000000000000000
χ6344-4-4-44-444-44-44444-4-4-4-40000-4-44000040000000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-24-44-4-2-2-222220000-2-22000024-4000000-2-2220000000000000000000000000000000000000000
χ6544-4-4-44-44-24-44-4-2-2-222220000-2-2200002-4400000022-2-20000000000000000000000000000000000000000
χ6644-4-4-44-44-2-44-44-2-2-22222000022-20000-200000000000000000023−23−2323000000000000000000000000000000
χ6744-4-4-44-44-2-44-44-2-2-22222000022-20000-2000000000000000000−232323−23000000000000000000000000000000
χ684-44-444-4-4-244-4-422-2-222-24-44-4-222-2-222-20000000000000000-220000000000000000000000000000000000
χ694-44-444-4-4-244-4-422-2-222-2-44-44-22222-2-2-200000000000000002-20000000000000000000000000000000000
χ704-44-4-4-44440000-44-44-44-40000000000000000000000000022−22000000000022−22−22220000000000000000000000
χ714-44-4-4-44440000-44-44-44-400000000000000000000000000−22220000000000−222222−220000000000000000000000
χ724-44-4-4-444-200002-22-22-22000000023−23−232300000000000000022−220000006−6−66−222−20000000000000000000000
χ734-44-4-4-444-200002-22-22-22000000023−23−2323000000000000000−2222000000−666−62−2−220000000000000000000000
χ744-44-4-4-444-200002-22-22-220000000−232323−2300000000000000022−22000000−666−6−222−20000000000000000000000
χ754-44-4-4-444-200002-22-22-220000000−232323−23000000000000000−22220000006−6−662−2−220000000000000000000000
χ764-4-444-4-4440000-44-4-44-440000000000000000000000000000000000000000004-400000000000000000000
χ774-4-444-4-4440000-44-4-44-44000000000000000000000000000000000000000000-4400000000000000000000
χ784-4-44-444-44-444-4-4-44-444-40000-44-4000040000000000000000000000000000000000000000000000000000
χ794-4-44-444-4-24-4-4422-22-2-220000-22-20000200004i−4i000000000000−2i2i−2i2i000000000000000000000000000000
χ804-4-44-444-4-24-4-4422-22-2-220000-22-2000020000−4i4i0000000000002i−2i2i−2i000000000000000000000000000000
χ814-4-44-444-4-2-444-422-22-2-2200002-220000-200000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ824-4-44-444-4-2-444-422-22-2-2200002-220000-2000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ8388-8-88-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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