Finite Group Databasebeta

← Group #10858316

Character table — Group #10858316

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666222244888812121212121212124444444446666881212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-111-1-111-1-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-111-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1111111-1-11-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-111-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-11111-1-111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-11111-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1111111-111-1-1-1-1-1-1111-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-22222-20000000000-2-2000000000000-2-222000000000000000-2000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-2-20000000000-2-200000000000022-2-20000000000000002000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000000022000000000000-2-2-2-20000000000000002000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-220000000000220000000000002222000000000000000-2000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-222-1-1-1-1-2-2111111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-2-1-1-1-1221111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100002-2-2221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-222-2-21111-2-211-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222211112211-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ292222-2-2-2-222-22-222-22-2-2-222-2-2000000220000-2-200000000022-2-20000000000000000000022-2-2000002-200000000
χ302222-2-2-2-222-22-222-22-2-2-222-2-2000000220000-2-200000000022-2-200000000000000000000-2-22200000-2200000000
χ312222-2-2-2-222-22-222-22-2-2-2-2-222000000220000-2-2000000000-2-2220000000000000000000022-2-200000-2200000000
χ322222-2-2-2-222-22-222-22-2-2-2-2-222000000220000-2-2000000000-2-22200000000000000000000-2-222000002-200000000
χ3322-2-22-22-2200002-22-2-22-200002i−2i−i2−i2i2i2002i2i−2i−2i002i2i−2i−2i0000000002−2000000−i2−i2i2i222−2−2002-22−22−2000000000000−i2i20
χ3422-2-22-22-2200002-22-2-22-200002i−2i−i2−i2i2i2002i2i−2i−2i00−2i−2i2i2i0000000002−2000000−i2−i2i2i222−2−200-22−22−22000000000000i2−i20
χ3522-2-22-22-2200002-22-2-22-200002i−2ii2i2−i2−i2002i2i−2i−2i002i2i−2i−2i000000000−22000000i2i2−i2−i2−2−222002-2−22−22000000000000i2−i20
χ3622-2-22-22-2200002-22-2-22-200002i−2ii2i2−i2−i2002i2i−2i−2i00−2i−2i2i2i000000000−22000000i2i2−i2−i2−2−22200-222−22−2000000000000−i2i20
χ3722-2-22-22-2200002-22-2-22-20000−2i2i−i2−i2i2i200−2i−2i2i2i002i2i−2i−2i000000000−22000000−i2−i2i2i2−2−22200-222−22−2000000000000i2−i20
χ3822-2-22-22-2200002-22-2-22-20000−2i2i−i2−i2i2i200−2i−2i2i2i00−2i−2i2i2i000000000−22000000−i2−i2i2i2−2−222002-2−22−22000000000000−i2i20
χ3922-2-22-22-2200002-22-2-22-20000−2i2ii2i2−i2−i200−2i−2i2i2i002i2i−2i−2i0000000002−2000000i2i2−i2−i222−2−200-22−22−22000000000000−i2i20
χ4022-2-22-22-2200002-22-2-22-20000−2i2ii2i2−i2−i200−2i−2i2i2i00−2i−2i2i2i0000000002−2000000i2i2−i2−i222−2−2002-22−22−2000000000000i2−i20
χ412-2-2222-2-222-2-22-2-2-22-22200000000002-200002-22i−2i2i−2i02-2000000000022-2-2000000002i−2i00000000000002i−2i000000
χ422-2-2222-2-222-2-22-2-2-22-22200000000002-200002-22i−2i2i−2i0-220000000000-2-222000000002i−2i0000000000000−2i2i000000
χ432-2-2222-2-222-2-22-2-2-22-22200000000002-200002-2−2i2i−2i2i02-2000000000022-2-200000000−2i2i0000000000000−2i2i000000
χ442-2-2222-2-222-2-22-2-2-22-22200000000002-200002-2−2i2i−2i2i0-220000000000-2-22200000000−2i2i00000000000002i−2i000000
χ452-2-2222-2-22-222-2-2-2-22-2222-22-2000000-220000-222i−2i2i−2i000002-22-20000000000000000−2i2i0000000000000002i−2i0000
χ462-2-2222-2-22-222-2-2-2-22-2222-22-2000000-220000-22−2i2i−2i2i000002-22-200000000000000002i−2i000000000000000−2i2i0000
χ472-2-2222-2-22-222-2-2-2-22-222-22-22000000-220000-222i−2i2i−2i00000-22-220000000000000000−2i2i000000000000000−2i2i0000
χ482-2-2222-2-22-222-2-2-2-22-222-22-22000000-220000-22−2i2i−2i2i00000-22-2200000000000000002i−2i0000000000000002i−2i0000
χ492-2-22-2-2222-2-222-2-2222-2-22-2-22002-22-2-2200002-200000002-22-2-22000000002-22-200000000000002-2000000000000
χ502-2-22-2-2222-2-222-2-2222-2-22-2-2200-22-22-2200002-20000000-222-2-2200000000-22-220000000000000-22000000000000
χ512-2-22-2-2222-2-222-2-2222-2-2-222-2002-22-2-2200002-20000000-22-222-2000000002-22-20000000000000-22000000000000
χ522-2-22-2-2222-2-222-2-2222-2-2-222-200-22-22-2200002-200000002-2-222-200000000-22-2200000000000002-2000000000000
χ532-2-22-2-222-1-2-22211-1-1-1112-2-22002-22-21-13−33−3-1100000002-2-111-1003−33−33−3-11-113−33−3000000000-113−30000000000
χ542-2-22-2-222-1-2-22211-1-1-1112-2-22002-22-21-1−33−33-1100000002-2-111-100−33−33−33-11-11−33−33000000000-11−330000000000
χ552-2-22-2-222-1-2-22211-1-1-1112-2-2200-22-221-13−33−3-110000000-22-111-1003−33−33−31-11-1−33−330000000001-1−330000000000
χ562-2-22-2-222-1-2-22211-1-1-1112-2-2200-22-221-1−33−33-110000000-22-111-100−33−33−331-11-13−33−30000000001-13−30000000000
χ572-2-22-2-222-1-2-22211-1-1-111-222-2002-22-21-13−33−3-110000000-221-1-11003−3−33−33-11-113−33−30000000001-1−330000000000
χ582-2-22-2-222-1-2-22211-1-1-111-222-2002-22-21-1−33−33-110000000-221-1-1100−333−33−3-11-11−33−330000000001-13−30000000000
χ592-2-22-2-222-1-2-22211-1-1-111-222-200-22-221-13−33−3-1100000002-21-1-11003−3−33−331-11-1−33−33000000000-113−30000000000
χ602-2-22-2-222-1-2-22211-1-1-111-222-200-22-221-1−33−33-1100000002-21-1-1100−333−33−31-11-13−33−3000000000-11−330000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-2220000-400000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000040000000000-2-200000000000000000000000000000000000
χ634444-4-4-4-44-44-4444-44-4-4-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-24-44-4-2-22-222244-4-4000000-2-2000022000000000-2-222000000000000000000000000000000000000000
χ654444-4-4-4-4-24-44-4-2-22-2222-4-444000000-2-200002200000000022-2-2000000000000000000000000000000000000000
χ664444-4-4-4-4-2-44-44-2-22-22220000000000220000-2-20000000000000000023−23−23230000000000000000000000000000000
χ674444-4-4-4-4-2-44-44-2-22-22220000000000220000-2-200000000000000000−232323−230000000000000000000000000000000
χ6844-4-44-44-4-20000-22-222-2200004i−4i−2i2−2i22i22i200−2i−2i2i2i00000000000000022−22000000i2i2−i2−i2−2−22200000000000000000000000
χ6944-4-44-44-4-20000-22-222-2200004i−4i2i22i2−2i2−2i200−2i−2i2i2i000000000000000−2222000000−i2−i2i2i222−2−200000000000000000000000
χ7044-4-44-44-4-20000-22-222-220000−4i4i−2i2−2i22i22i2002i2i−2i−2i000000000000000−2222000000i2i2−i2−i222−2−200000000000000000000000
χ7144-4-44-44-4-20000-22-222-220000−4i4i2i22i2−2i2−2i2002i2i−2i−2i00000000000000022−22000000−i2−i2i2i2−2−22200000000000000000000000
χ7244-4-4-44-44400004-4-4-44-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7344-4-4-44-44400004-4-4-44-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ744-44-44-4-4440000-44-4-444-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ754-44-44-4-4440000-44-4-444-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ764-44-4-444-440000-444-4-4-44000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ774-44-4-444-440000-444-4-4-440000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ784-44-4-444-4-200002-2-2222-2000000−2i22i22i2−2i200−2i32i32i3−2i300000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ794-44-4-444-4-200002-2-2222-2000000−2i22i22i2−2i2002i3−2i3−2i32i300000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ804-44-4-444-4-200002-2-2222-20000002i2−2i2−2i22i200−2i32i32i3−2i300000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ814-44-4-444-4-200002-2-2222-20000002i2−2i2−2i22i2002i3−2i3−2i32i300000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ824-4-4444-4-4-24-4-44222-22-2-20000000000-220000-22000004-40000000000-2-2220000000000000000000000000000000
χ834-4-4444-4-4-24-4-44222-22-2-20000000000-220000-2200000-44000000000022-2-20000000000000000000000000000000
χ844-4-4444-4-4-2-444-4222-22-2-24-44-40000002-200002-2000000000-22-22000000000000000000000000000000000000000
χ854-4-4444-4-4-2-444-4222-22-2-2-44-440000002-200002-20000000002-22-2000000000000000000000000000000000000000
χ864-4-44-4-444444-4-4-4-4444-4-400000000004-40000-440000000000000000000000000000000000000000000000000000
χ874-4-44-4-444-244-4-422-2-2-2220000000000-2223−2323−232-2000000000000000−232300000000000000000000000000000000000
χ884-4-44-4-444-244-4-422-2-2-2220000000000-22−2323−23232-200000000000000023−2300000000000000000000000000000000000
χ8988-8-8-88-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000000000

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