Finite Group Databasebeta

← Group #10858773

Character table — Group #10858773

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666444444888812121212121212122222224446666881212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-111-1-1-1-111-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111111-1-11111-1-1111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-2222200-2000000000000-2-20000000022-2-20000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-200-2000000000000-2-200000000-2-2220000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000000002200000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2002000000000000220000000022220000000000000-200000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-2-2221111-2-2-1-1-1-111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-2111122-1-1-1-1111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-21111221111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-21111-1-111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-1000022-222-1-1-1-1221111111111-1-1-1-100000000-2-1-1110000000000
χ2922-2-222-2-2222-2-222-22-2-2-20000000000220000-2-222-2-22-200022-2-20000000000000000002-20000000002-200000000
χ3022-2-222-2-2222-2-222-22-2-2-20000000000220000-2-222-2-2-22000-2-2220000000000000000002-2000000000-2200000000
χ3122-2-222-2-2222-2-222-22-2-2-20000000000220000-2-2-2-2222-200022-2-2000000000000000000-22000000000-2200000000
χ3222-2-222-2-2222-2-222-22-2-2-20000000000220000-2-2-2-222-22000-2-222000000000000000000-220000000002-200000000
χ3322-2-222-2-22-2-22222-22-2-2-22i2i−2i−2i000000-2-200002222-2-2000000000002i2i−2i−2i000000000000-22000000000002i−2i000000
χ3422-2-222-2-22-2-22222-22-2-2-22i2i−2i−2i000000-2-2000022-2-222000000000002i2i−2i−2i0000000000002-200000000000−2i2i000000
χ3522-2-222-2-22-2-22222-22-2-2-2−2i−2i2i2i000000-2-200002222-2-200000000000−2i−2i2i2i000000000000-2200000000000−2i2i000000
χ3622-2-222-2-22-2-22222-22-2-2-2−2i−2i2i2i000000-2-2000022-2-22200000000000−2i−2i2i2i0000000000002-2000000000002i−2i000000
χ372-22-22-22-222-22-2-2-2-22-2222-22-20000002-200002-20000000000000002-22-2000000000000002i2i−2i−2i00000000002i−2i000
χ382-22-22-22-222-22-2-2-2-22-2222-22-20000002-200002-20000000000000002-22-200000000000000−2i−2i2i2i0000000000−2i2i000
χ392-22-22-22-222-22-2-2-2-22-222-22-220000002-200002-2000000000000000-22-22000000000000002i2i−2i−2i0000000000−2i2i000
χ402-22-22-22-222-22-2-2-2-22-222-22-220000002-200002-2000000000000000-22-2200000000000000−2i−2i2i2i00000000002i−2i000
χ412-2-222-2-222-222-2-2-2222-2-22i−2i−2i2i002i2i−2i−2i-2200002-200000002-20000002i−2i−2i2i002i2i−2i−2i00000000000002-2000000000000
χ422-2-222-2-222-222-2-2-2222-2-22i−2i−2i2i00−2i−2i2i2i-2200002-20000000-220000002i−2i−2i2i00−2i−2i2i2i0000000000000-22000000000000
χ432-2-222-2-222-222-2-2-2222-2-2−2i2i2i−2i002i2i−2i−2i-2200002-20000000-22000000−2i2i2i−2i002i2i−2i−2i0000000000000-22000000000000
χ442-2-222-2-222-222-2-2-2222-2-2−2i2i2i−2i00−2i−2i2i2i-2200002-200000002-2000000−2i2i2i−2i00−2i−2i2i2i00000000000002-2000000000000
χ452-2-222-2-22-1-222-211-1-1-1112i−2i−2i2i002i2i−2i−2i1-133−3−3-1100000002-2−i3i3−i3i300−iii−i3−3−i−iii−i3−i3i3i3000000000-113−30000000000
χ462-2-222-2-22-1-222-211-1-1-1112i−2i−2i2i002i2i−2i−2i1-1−3−333-1100000002-2i3−i3i3−i300−iii−i−33−i−iiii3i3−i3−i3000000000-11−330000000000
χ472-2-222-2-22-1-222-211-1-1-1112i−2i−2i2i00−2i−2i2i2i1-133−3−3-110000000-22−i3i3−i3i300−iii−i3−3ii−i−ii3i3−i3−i30000000001-1−330000000000
χ482-2-222-2-22-1-222-211-1-1-1112i−2i−2i2i00−2i−2i2i2i1-1−3−333-110000000-22i3−i3i3−i300−iii−i−33ii−i−i−i3−i3i3i30000000001-13−30000000000
χ492-2-222-2-22-1-222-211-1-1-111−2i2i2i−2i002i2i−2i−2i1-133−3−3-110000000-22i3−i3i3−i300i−i−ii3−3−i−iii−i3−i3i3i30000000001-1−330000000000
χ502-2-222-2-22-1-222-211-1-1-111−2i2i2i−2i002i2i−2i−2i1-1−3−333-110000000-22−i3i3−i3i300i−i−ii−33−i−iiii3i3−i3−i30000000001-13−30000000000
χ512-2-222-2-22-1-222-211-1-1-111−2i2i2i−2i00−2i−2i2i2i1-133−3−3-1100000002-2i3−i3i3−i300i−i−ii3−3ii−i−ii3i3−i3−i3000000000-113−30000000000
χ522-2-222-2-22-1-222-211-1-1-111−2i2i2i−2i00−2i−2i2i2i1-1−3−333-1100000002-2−i3i3−i3i300i−i−ii−33ii−i−i−i3−i3i3i3000000000-11−330000000000
χ532-2-22-222-2200002-22-2-22-200002-2−i2i2−i2i2002-22-2002-22-2000000000−i2i2000000−i2i2−i2i2−i2i2−i2i22-200−i2i2−i2i2000000000000−i2i20
χ542-2-22-222-2200002-22-2-22-200002-2−i2i2−i2i2002-22-200-22-22000000000−i2i2000000−i2i2−i2i2−i2i2−i2i2-2200i2−i2i2−i2000000000000i2−i20
χ552-2-22-222-2200002-22-2-22-200002-2i2−i2i2−i2002-22-2002-22-2000000000i2−i2000000i2−i2i2−i2i2−i2i2−i22-200i2−i2i2−i2000000000000i2−i20
χ562-2-22-222-2200002-22-2-22-200002-2i2−i2i2−i2002-22-200-22-22000000000i2−i2000000i2−i2i2−i2i2−i2i2−i2-2200−i2i2−i2i2000000000000−i2i20
χ572-2-22-222-2200002-22-2-22-20000-22−i2i2−i2i200-22-22002-22-2000000000i2−i2000000−i2i2−i2i2i2−i2i2−i2-2200−i2i2−i2i2000000000000i2−i20
χ582-2-22-222-2200002-22-2-22-20000-22−i2i2−i2i200-22-2200-22-22000000000i2−i2000000−i2i2−i2i2i2−i2i2−i22-200i2−i2i2−i2000000000000−i2i20
χ592-2-22-222-2200002-22-2-22-20000-22i2−i2i2−i200-22-22002-22-2000000000−i2i2000000i2−i2i2−i2−i2i2−i2i2-2200i2−i2i2−i2000000000000−i2i20
χ602-2-22-222-2200002-22-2-22-20000-22i2−i2i2−i200-22-2200-22-22000000000−i2i2000000i2−i2i2−i2−i2i2−i2i22-200−i2i2−i2i2000000000000i2−i20
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-222000000-4000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-40000222222220000004000000000000-2-20000000000000000000000000000000
χ634444-4-4-4-440000-444-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ644444-4-4-4-440000-444-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ654444-4-4-4-4-200002-2-2222-200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ664444-4-4-4-4-200002-2-2222-200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ674444-4-4-4-4-200002-2-2222-2000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ684444-4-4-4-4-200002-2-2222-2000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ6944-4-444-4-4-244-4-4-2-22-22220000000000-2-200002200004-4000-2-222000000000000000000000000000000000000000
χ7044-4-444-4-4-244-4-4-2-22-22220000000000-2-20000220000-4400022-2-2000000000000000000000000000000000000000
χ7144-4-444-4-4-2-4-444-2-22-22224i4i−4i−4i000000220000-2-2000000000000000−2i−2i2i2i000000000000000000000000000000000
χ7244-4-444-4-4-2-4-444-2-22-2222−4i−4i4i4i000000220000-2-20000000000000002i2i−2i−2i000000000000000000000000000000000
χ7344-4-4-4-44440000-44-4-444-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7444-4-4-4-44440000-44-4-444-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ754-44-44-44-44-44-44-4-4-44-4440000000000-440000-440000000000000000000000000000000000000000000000000000
χ764-44-44-44-4-24-44-4222-22-2-24-44-4000000-220000-22000000000000000-22-22000000000000000000000000000000000
χ774-44-44-44-4-24-44-4222-22-2-2-44-44000000-220000-220000000000000002-22-2000000000000000000000000000000000
χ784-44-44-44-4-2-44-44222-22-2-200000000002-200002-2000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ794-44-44-44-4-2-44-44222-22-2-200000000002-200002-20000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ804-44-4-44-44400004-4-4-44-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ814-44-4-44-44400004-4-4-44-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ824-4-444-4-4444-4-44-4-4444-4-400000000004-40000-440000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-24-4-4422-2-2-2220000000000-222323−23−232-20000000000000000000−23230000000000000000000000000000000
χ844-4-444-4-44-24-4-4422-2-2-2220000000000-22−23−2323232-2000000000000000000023−230000000000000000000000000000000
χ854-4-44-444-4-20000-22-222-2200004-4−2i22i2−2i22i200-22-22000000000000000−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ864-4-44-444-4-20000-22-222-2200004-42i2−2i22i2−2i200-22-220000000000000002i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ874-4-44-444-4-20000-22-222-220000-44−2i22i2−2i22i2002-22-20000000000000002i2−2i2000000i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ884-4-44-444-4-20000-22-222-220000-442i2−2i22i2−2i2002-22-2000000000000000−2i22i2000000−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ8988-8-8-8-888-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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