Finite Group Databasebeta

← Group #88430

Character table — Group #88430

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size111122226666666612121212181818181818181818181818181818181818
order12443612123366121212123612122466888812122424242424242424
χ111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ511-1-111-1-11111-1-1-1-111-1-11-111i−ii−i-1-1ii−i−iii−i−i
χ611-1-111-1-11111-1-1-1-111-1-11-111−ii−ii-1-1−i−iii−i−iii
χ711-1-111-1-11111-1-1-1-111-1-1-11-1-1i−i−ii11ii−i−i−i−iii
χ811-1-111-1-11111-1-1-1-111-1-1-11-1-1−iii−i11−i−iiiii−i−i
χ9222222222-12-1-1-122-1-1-1-122-1-10000-1-100000000
χ10222222222-12-1-1-122-1-1-1-1-2-21100001100000000
χ1122222222-12-1222-1-1-1-1-1-100000022000000-1-1-1-1
χ1222222222-12-1222-1-1-1-1-1-1000000-2-20000001111
χ1322-2-222-2-22-12-111-2-2-1-1112-2-1-100001100000000
χ1422-2-222-2-22-12-111-2-2-1-111-22110000-1-100000000
χ1522-2-222-2-2-12-12-2-211-1-1110000002i−2i000000−i−iii
χ1622-2-222-2-2-12-12-2-211-1-111000000−2i2i000000ii−i−i
χ172-22i−2i2-22i−2i22-2-22i−2i2i−2i2-22i−2i000000000000000000
χ182-22i−2i2-22i−2i2-1-21−ii2i−2i-11−ii00−i3i300003−300000000
χ192-22i−2i2-22i−2i2-1-21−ii2i−2i-11−ii00i3−i30000−3300000000
χ202-22i−2i2-22i−2i-121-22i−2i−ii-11−ii00000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ212-22i−2i2-22i−2i-121-22i−2i−ii-11−ii00000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ222-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i000000000000000000
χ232-2−2i2i2-2−2i2i2-1-21i−i−2i2i-11i−i00−i3i30000−3300000000
χ242-2−2i2i2-2−2i2i2-1-21i−i−2i2i-11i−i00i3−i300003−300000000
χ252-2−2i2i2-2−2i2i-121-2−2i2ii−i-11i−i00000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ262-2−2i2i2-2−2i2i-121-2−2i2ii−i-11i−i00000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ2744444444-2-2-2-2-2-2-2-21111000000000000000000
χ2844-4-444-4-4-2-2-2-2222211-1-1000000000000000000
χ294-44i−4i4-44i−4i-2-222−2i2i−2i2i1-1i−i000000000000000000
χ304-4−4i4i4-4−4i4i-2-2222i−2i2i−2i1-1−ii000000000000000000
χ316666-3-3-3-30000000000000000220000-1-1-1-10000
χ326666-3-3-3-30000000000000000-2-2000011110000
χ3366-6-6-3-33300000000000000002i−2i0000−i−iii0000
χ3466-6-6-3-3330000000000000000−2i2i0000ii−i−i0000
χ356-66i−6i-33−3i3i0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ366-66i−6i-33−3i3i0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ376-6−6i6i-333i−3i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ386-6−6i6i-333i−3i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000

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