Finite Group Databasebeta

← Group #13135098

Character table — Group #13135098

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1244234666888812121212242424243366121212122424242424242424366666121212121212242424242424242424242424246688121216161616161616162424242448484848484848484848484848484848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-111-1111ii−i−i-1-1-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-111i−i-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1011-1-111-1111ii−i−i-1-1-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-111i−i-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1111-1-111-1111ii−i−i-1-1-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-1−ii11ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1211-1-111-1111ii−i−i-1-1-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-1−ii11−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1311-1-111-1111−i−iii-1-1-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-111−ii-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1411-1-111-1111−i−iii-1-1-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-111−ii-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1511-1-111-1111−i−iii-1-1-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1-1i−i11−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1611-1-111-1111−i−iii-1-1-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1-1i−i11ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1722222222222222222222222-12-122-1-122-1-122-1-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-12-122-1-122-1-122-1-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000011111111
χ192222222222222222222222-12-12-1-122-1-122-1-122-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-100000000222200000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-12-1-122-1-122-1-122-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-100000000-2-2-2-2000000001111111100000000
χ212222222222-2-2-2-22222-2-2-2-22-12-122-1-1-2-211-2-211-12-1-1-1-12-1-1-1-1-1-21-21111111110000000000002i2i−2i−2i000000000000−i−i−i−iiiii
χ222222222222-2-2-2-22222-2-2-2-22-12-122-1-1-2-211-2-211-12-1-1-1-12-1-1-1-1-1-21-2111111111000000000000−2i−2i2i2i000000000000iiii−i−i−i−i
χ232222222222-2-2-2-22222-2-2-2-2-12-12-1-12211-2-211-2-2-1-12-1-1-1-12-1-1-1-11-21-211111111000000002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ242222222222-2-2-2-22222-2-2-2-2-12-12-1-12211-2-211-2-2-1-12-1-1-1-12-1-1-1-11-21-21111111100000000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ252222-22-2-2-222-22-2-2-2222-22-22222222222-2-222-2-22-2-2-2-22-2-2-2-222-22-2222-2-222-2-2000000000000000000000000000000000000
χ262222-22-2-2-222-22-2-2-2222-22-22-12-122-1-122112211-1-2111-1-2111-1-1-2-1-2-1-1-111-1-11100000000000000000000000000003−33−33−33−3
χ272222-22-2-2-222-22-2-2-2222-22-22-12-122-1-122112211-1-2111-1-2111-1-1-2-1-2-1-1-111-1-1110000000000000000000000000000−33−33−33−33
χ282222-22-2-2-222-22-2-2-2222-22-2-12-12-1-122-1-1-2-2-1-1-2-2-11-211-11-211-1-11212-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ292222-22-2-2-222-22-2-2-2222-22-2-12-12-1-122-1-1-2-2-1-1-2-2-11-211-11-211-1-11212-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ302222-22-2-2-22-22-22-2-222-22-2222222222-2-222-2-2222-2-2-2-22-2-2-2-2222-22-2-2-222-2-222000000000000000000000000000000000000
χ312222-22-2-2-22-22-22-2-222-22-222-12-122-1-1-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1212111-1-111-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ322222-22-2-2-22-22-22-2-222-22-222-12-122-1-1-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1212111-1-111-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ332222-22-2-2-22-22-22-2-222-22-22-12-12-1-12211221122-11-211-11-211-1-1-1-2-1-211-1-111-1-1000000000000000000003−33−3−33−3300000000
χ342222-22-2-2-22-22-22-2-222-22-22-12-12-1-12211221122-11-211-11-211-1-1-1-2-1-211-1-111-1-100000000000000000000−33−333−33−300000000
χ3522-2-222-22222i2i−2i−2i-2-2-2-22i2i−2i−2i2-12-1-2-2112i2i−i−i−2i−2iii-12-1-1-1-1-2111112i−i−2ii−i−i−i−iiiii0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ3622-2-222-22222i2i−2i−2i-2-2-2-22i2i−2i−2i2-12-1-2-2112i2i−i−i−2i−2iii-12-1-1-1-1-2111112i−i−2ii−i−i−i−iiiii000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ3722-2-222-22222i2i−2i−2i-2-2-2-22i2i−2i−2i-12-1211-2-2−i−i2i2iii−2i−2i-1-12-1-1-11-21111−i2ii−2i−i−i−i−iiiii000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000
χ3822-2-222-22222i2i−2i−2i-2-2-2-22i2i−2i−2i-12-1211-2-2−i−i2i2iii−2i−2i-1-12-1-1-11-21111−i2ii−2i−i−i−i−iiiii00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000
χ3922-2-222-2222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-12-1-2-211−2i−2iii2i2i−i−i-12-1-1-1-1-211111−2ii2i−iiiii−i−i−i−i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ4022-2-222-2222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-12-1-2-211−2i−2iii2i2i−i−i-12-1-1-1-1-211111−2ii2i−iiiii−i−i−i−i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ4122-2-222-2222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-12-1211-2-2ii−2i−2i−i−i2i2i-1-12-1-1-11-21111i−2i−i2iiiii−i−i−i−i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000
χ4222-2-222-2222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-12-1211-2-2ii−2i−2i−i−i2i2i-1-12-1-1-11-21111i−2i−i2iiiii−i−i−i−i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000
χ4322-2-2-222-2-222i−2i−2i2i22-2-22i−2i−2i2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i2-2-2-2-222222-2-2−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4422-2-2-222-2-222i−2i−2i2i22-2-22i−2i−2i2i2-12-1-2-2112i2iii−2i−2i−i−i-1-2111-12-1-1-111−2i−i2ii−i−iiiii−i−i0000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23
χ4522-2-2-222-2-222i−2i−2i2i22-2-22i−2i−2i2i2-12-1-2-2112i2iii−2i−2i−i−i-1-2111-12-1-1-111−2i−i2ii−i−iiiii−i−i0000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23
χ4622-2-2-222-2-222i−2i−2i2i22-2-22i−2i−2i2i-12-1211-2-2−i−i−2i−2iii2i2i-11-211-1-12-1-111i2i−i−2i−i−iiiii−i−i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ4722-2-2-222-2-222i−2i−2i2i22-2-22i−2i−2i2i-12-1211-2-2−i−i−2i−2iii2i2i-11-211-1-12-1-111i2i−i−2i−i−iiiii−i−i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ4822-2-2-222-2-22−2i2i2i−2i22-2-2−2i2i2i−2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2-2-2-2-222222-2-22i−2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4922-2-2-222-2-22−2i2i2i−2i22-2-2−2i2i2i−2i2-12-1-2-211−2i−2i−i−i2i2iii-1-2111-12-1-1-1112ii−2i−iii−i−i−i−iii0000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13
χ5022-2-2-222-2-22−2i2i2i−2i22-2-2−2i2i2i−2i2-12-1-2-211−2i−2i−i−i2i2iii-1-2111-12-1-1-1112ii−2i−iii−i−i−i−iii0000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13
χ5122-2-2-222-2-22−2i2i2i−2i22-2-2−2i2i2i−2i-12-1211-2-2ii2i2i−i−i−2i−2i-11-211-1-12-1-111−i−2ii2iii−i−i−i−iii00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ5222-2-2-222-2-22−2i2i2i−2i22-2-2−2i2i2i−2i-12-1211-2-2ii2i2i−i−i−2i−2i-11-211-1-12-1-111−i−2ii2iii−i−i−i−iii00000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-2-21111-2-2-2-211111111000000000000000000000000000000000000
χ544444444444-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2111-2-211112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-44-4-4-444-44-4-4-4444-44-4-2-2-2-2-2-2-2-2-2-222-2-222122-1-1122-1-1112-22-211-1-111-1-1000000000000000000000000000000000000
χ564444-44-4-4-44-44-44-4-444-44-44-2-2-2-2-2-2-2-222-2-222-2-2122-1-1122-1-111-22-22-1-111-1-111000000000000000000000000000000000000
χ5744-4-444-44444i4i−4i−4i-4-4-4-44i4i−4i−4i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i1-2-211122-1-1-1-1−2i−2i2i2iiiii−i−i−i−i000000000000000000000000000000000000
χ5844-4-444-4444−4i−4i4i4i-4-4-4-4−4i−4i4i4i-2-2-2-222222i2i2i2i−2i−2i−2i−2i1-2-211122-1-1-1-12i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
χ5944-4-4-444-4-444i−4i−4i4i44-4-44i−4i−4i4i-2-2-2-22222−2i−2i2i2i2i2i−2i−2i122-1-11-2-211-1-12i−2i−2i2iii−i−i−i−iii000000000000000000000000000000000000
χ6044-4-4-444-4-44−4i4i4i−4i44-4-4−4i4i4i−4i-2-2-2-222222i2i−2i−2i−2i−2i2i2i122-1-11-2-211-1-1−2i2i2i−2i−i−iiiii−i−i000000000000000000000000000000000000
χ614-44i−4i04000-40000004i−4i000044-4-44i−4i4i−4i0000000040000-400004i−4i000000000000000000000000000000000000000000000000
χ624-44i−4i04000-40000004i−4i00004-2-424i−4i−2i2i00−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13-2000020000−2i2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ634-44i−4i04000-40000004i−4i00004-2-424i−4i−2i2i002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13-2000020000−2i2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.