Finite Group Databasebeta

← Group #11714115

Character table — Group #11714115

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122222222222222333366666666666666888888888888888888888888888888884848484848484848
order12224444448888888822224444448888888836661212121212121212121212122424242424242424242424242424242444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-11-11-1
χ61111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-11-11
χ71111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-111-1-11
χ81111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-111-1
χ9222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ102222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000
χ11222222-2-2-2-2000000002222-2-222-2-20000000022222222-2-2-2-2-2-2-2-2000000000000000000000000
χ12222222-2-2-2-2000000002222-2-222-2-200000000-1-1-1-1-1-1-1-1111111113333−3−3−3−33333−3−3−3−300000000
χ13222222-2-2-2-2000000002222-2-222-2-200000000-1-1-1-1-1-1-1-111111111−3−3−3−33333−3−3−3−3333300000000
χ142222-2-222-2-2000000002222-2-2-2-222000000002222-2-2-2-22222-2-2-2-2000000000000000000000000
χ152222-2-222-2-2000000002222-2-2-2-22200000000-1-1-1-11111-1-1-1-111113333−3−3−3−3−3−3−3−3333300000000
χ162222-2-222-2-2000000002222-2-2-2-22200000000-1-1-1-11111-1-1-1-11111−3−3−3−333333333−3−3−3−300000000
χ172222-2-2-2-2222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000
χ182222-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-100000000
χ1922-2-200002-2000022-2-222-2-22-20000000022-2-222-2-20000000022-2-20000000022-2-222-2-200000000
χ2022-2-200002-2000022-2-222-2-22-20000000022-2-2-1-11133−3−333−3−3-1-11133−3−333−3−3-1-111-1-11100000000
χ2122-2-200002-2000022-2-222-2-22-20000000022-2-2-1-111−3−333−3−333-1-111−3−333−3−333-1-111-1-11100000000
χ2222-2-200002-20000-2-22222-2-22-200000000-2-22222-2-20000000022-2-200000000-2-222-2-22200000000
χ2322-2-200002-20000-2-22222-2-22-200000000-2-222-1-11133−3−333−3−3-1-111−3−333−3−33311-1-111-1-100000000
χ2422-2-200002-20000-2-22222-2-22-200000000-2-222-1-111−3−333−3−333-1-11133−3−333−3−311-1-111-1-100000000
χ2522-2-20000-2222-2-2000022-2-2-22000022-2-2000022-2-200000000-2-22222-2-2-2-2220000000000000000
χ2622-2-20000-2222-2-2000022-2-2-22000022-2-20000-1-11133−3−3−3−33311-1-1-1-11111-1-1−3−33333−3−300000000
χ2722-2-20000-2222-2-2000022-2-2-22000022-2-20000-1-111−3−33333−3−311-1-1-1-11111-1-133−3−3−3−33300000000
χ2822-2-20000-22-2-222000022-2-2-220000-2-222000022-2-200000000-2-222-2-22222-2-20000000000000000
χ2922-2-20000-22-2-222000022-2-2-220000-2-2220000-1-11133−3−3−3−33311-1-111-1-1-1-11133−3−3−3−33300000000
χ3022-2-20000-22-2-222000022-2-2-220000-2-2220000-1-111−3−33333−3−311-1-111-1-1-1-111−3−33333−3−300000000
χ312-22-2002i−2i002−22−2−i2i2−i2i22-22-200002i−2i2−22−2−i2i2−i2i22-22-200002i−2i2i−2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ322-22-2002i−2i002−22−2−i2i2−i2i22-22-200002i−2i2−22−2−i2i2−i2i2-11-11−i3i3−i3i3−ii−ii3−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ332-22-2002i−2i002−22−2−i2i2−i2i22-22-200002i−2i2−22−2−i2i2−i2i2-11-11i3−i3i3−i3−ii−ii−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ342-22-2002i−2i00−22−22i2−i2i2−i22-22-200002i−2i−22−22i2−i2i2−i22-22-200002i−2i2i−2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ352-22-2002i−2i00−22−22i2−i2i2−i22-22-200002i−2i−22−22i2−i2i2−i2-11-11−i3i3−i3i3−ii−ii3−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ362-22-2002i−2i00−22−22i2−i2i2−i22-22-200002i−2i−22−22i2−i2i2−i2-11-11i3−i3i3−i3−ii−ii−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ372-22-200−2i2i002−22−2i2−i2i2−i22-22-20000−2i2i2−22−2i2−i2i2−i22-22-20000−2i2i−2i2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ382-22-200−2i2i002−22−2i2−i2i2−i22-22-20000−2i2i2−22−2i2−i2i2−i2-11-11−i3i3−i3i3i−ii−i−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ392-22-200−2i2i002−22−2i2−i2i2−i22-22-20000−2i2i2−22−2i2−i2i2−i2-11-11i3−i3i3−i3i−ii−i3−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ402-22-200−2i2i00−22−22−i2i2−i2i22-22-20000−2i2i−22−22−i2i2−i2i22-22-20000−2i2i−2i2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ412-22-200−2i2i00−22−22−i2i2−i2i22-22-20000−2i2i−22−22−i2i2−i2i2-11-11−i3i3−i3i3i−ii−i−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ422-22-200−2i2i00−22−22−i2i2−i2i22-22-20000−2i2i−22−22−i2i2−i2i2-11-11i3−i3i3−i3i−ii−i3−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ432-2-222i−2i00002−2−22−i2i2i2−i22-2-22002i−2i002−2−22−i2i2i2−i22-2-22−2i2i2i−2i000000002−2−22−222−2−i2i2i2−i2−i2i2i2−i200000000
χ442-2-222i−2i00002−2−22−i2i2i2−i22-2-22002i−2i002−2−22−i2i2i2−i2-111-1i−i−ii−i3i3i3−i33−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ452-2-222i−2i00002−2−22−i2i2i2−i22-2-22002i−2i002−2−22−i2i2i2−i2-111-1i−i−iii3−i3−i3i3−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ462-2-222i−2i0000−222−2i2−i2−i2i22-2-22002i−2i00−222−2i2−i2−i2i22-2-22−2i2i2i−2i00000000−222−22−2−22i2−i2−i2i2i2−i2−i2i200000000
χ472-2-222i−2i0000−222−2i2−i2−i2i22-2-22002i−2i00−222−2i2−i2−i2i2-111-1i−i−ii−i3i3i3−i33−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ482-2-222i−2i0000−222−2i2−i2−i2i22-2-22002i−2i00−222−2i2−i2−i2i2-111-1i−i−iii3−i3−i3i3−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ492-2-22−2i2i00002−2−22i2−i2−i2i22-2-2200−2i2i002−2−22i2−i2−i2i22-2-222i−2i−2i2i000000002−2−22−222−2i2−i2−i2i2i2−i2−i2i200000000
χ502-2-22−2i2i00002−2−22i2−i2−i2i22-2-2200−2i2i002−2−22i2−i2−i2i2-111-1−iii−i−i3i3i3−i3−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ512-2-22−2i2i00002−2−22i2−i2−i2i22-2-2200−2i2i002−2−22i2−i2−i2i2-111-1−iii−ii3−i3−i3i33−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ522-2-22−2i2i0000−222−2−i2i2i2−i22-2-2200−2i2i00−222−2−i2i2i2−i22-2-222i−2i−2i2i00000000−222−22−2−22−i2i2i2−i2−i2i2i2−i200000000
χ532-2-22−2i2i0000−222−2−i2i2i2−i22-2-2200−2i2i00−222−2−i2i2i2−i2-111-1−iii−i−i3i3i3−i3−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ542-2-22−2i2i0000−222−2−i2i2i2−i22-2-2200−2i2i00−222−2−i2i2i2−i2-111-1−iii−ii3−i3−i3i33−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ55333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000001111-1-1-1-1
χ56333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000-1-1-1-11111
χ573333333333-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1111111110000000000000000000000000000000011-1-1-1-111
χ583333333333-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-11111111100000000000000000000000000000000-1-11111-1-1
χ593333-3-3-3-3333333-3-3-3-3-1-1-1-1-1-11111-1-1-1-11111000000000000000000000000000000001-11-1-11-11
χ603333-3-3-3-3333333-3-3-3-3-1-1-1-1-1-11111-1-1-1-1111100000000000000000000000000000000-11-111-11-1
χ613333-3-3-3-333-3-3-3-33333-1-1-1-1-1-111111111-1-1-1-1000000000000000000000000000000001-1-11-111-1
χ623333-3-3-3-333-3-3-3-33333-1-1-1-1-1-111111111-1-1-1-100000000000000000000000000000000-111-11-1-11
χ63666666-6-6-6-600000000-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ646666-6-666-6-600000000-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ6566-6-600006-6000066-6-6-2-222-2200000000-2-2220000000000000000000000000000000000000000
χ6666-6-600006-60000-6-666-2-222-220000000022-2-20000000000000000000000000000000000000000
χ6766-6-60000-6666-6-60000-2-2222-20000-2-22200000000000000000000000000000000000000000000
χ6866-6-60000-66-6-6660000-2-2222-2000022-2-200000000000000000000000000000000000000000000
χ696-66-6006i−6i0032−3232−32−3i23i2−3i23i2-22-220000−2i2i−22−22i2−i2i2−i20000000000000000000000000000000000000000
χ706-66-6006i−6i00−3232−32323i2−3i23i2−3i2-22-220000−2i2i2−22−2−i2i2−i2i20000000000000000000000000000000000000000
χ716-66-600−6i6i0032−3232−323i2−3i23i2−3i2-22-2200002i−2i−22−22−i2i2−i2i20000000000000000000000000000000000000000
χ726-66-600−6i6i00−3232−3232−3i23i2−3i23i2-22-2200002i−2i2−22−2i2−i2i2−i20000000000000000000000000000000000000000
χ736-6-666i−6i000032−32−3232−3i23i23i2−3i2-222-200−2i2i00−222−2i2−i2−i2i20000000000000000000000000000000000000000
χ746-6-666i−6i0000−323232−323i2−3i2−3i23i2-222-200−2i2i002−2−22−i2i2i2−i20000000000000000000000000000000000000000
χ756-6-66−6i6i000032−32−32323i2−3i2−3i23i2-222-2002i−2i00−222−2−i2i2i2−i20000000000000000000000000000000000000000
χ766-6-66−6i6i0000−323232−32−3i23i23i2−3i2-222-2002i−2i002−2−22i2−i2−i2i20000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.