Finite Group Databasebeta

← Group #88608

Character table — Group #88608

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size11222222226888888888888888888121212125454108
order1233336666499999999918181818181818181812121212884
χ1111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1
χ322222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000
χ4222-1-1-12-1-1-12ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ682-1-1-1000
χ5222-1-1-12-1-1-12ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ682-1-1-1000
χ6222-1-1-12-1-1-12−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ522-1-1-1000
χ722-12-1-1-12-1-12ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-12-1-1000
χ822-12-1-1-12-1-12ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-12-1-1000
χ922-12-1-1-12-1-12−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-12-1-1000
χ1022-1-12-1-1-12-12ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68-1-12-1000
χ1122-1-12-1-1-12-12ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68-1-12-1000
χ1222-1-12-1-1-12-12−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52-1-12-1000
χ1322-1-1-12-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-12-1-1-12000
χ1422-1-1-12-1-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-12000
χ1522-1-1-12-1-1-122-1-122-1-1-12-1-1-122-1-1-12-1-1-1-12000
χ162-22222-2-2-2-20-1-1-1-1-1-1-1-1-111111111100002−20
χ172-22222-2-2-2-20-1-1-1-1-1-1-1-1-11111111110000−220
χ183333333333-1000000000000000000-1-1-1-111-1
χ193333333333-1000000000000000000-1-1-1-1-1-11
χ204-44444-4-4-4-40111111111-1-1-1-1-1-1-1-1-10000000
χ214-44-2-2-2-42220−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ680000000
χ224-44-2-2-2-42220ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ520000000
χ234-44-2-2-2-42220−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ680000000
χ244-4-24-2-22-4220−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000000
χ254-4-24-2-22-4220ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000000
χ264-4-24-2-22-4220−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000000
χ274-4-2-24-222-420−ζ44+ζ52−ζ68ζ4+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ4+ζ44−ζ52−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ44+ζ52−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ680000000
χ284-4-2-24-222-420ζ4+ζ68−ζ4+ζ44−ζ52−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ44+ζ52−ζ68ζ4+ζ68−ζ44+ζ52−ζ68ζ4+ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ520000000
χ294-4-2-24-222-420−ζ4+ζ44−ζ52−ζ44+ζ52−ζ68ζ4+ζ68−ζ44+ζ52−ζ68ζ4+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ4+ζ44−ζ52−ζ44+ζ52−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ68−ζ4−ζ68ζ44−ζ52+ζ68−ζ4−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4−ζ44+ζ52ζ44−ζ52+ζ680000000
χ304-4-2-2-24222-4011-2-2111-21-1-122-1-1-12-10000000
χ314-4-2-2-24222-401-2111-2-211-12-1-1-122-1-10000000
χ324-4-2-2-24222-40-2111-2111-22-1-1-12-1-1-120000000
χ33666-3-3-36-3-3-3-2000000000000000000-2111000
χ3466-36-3-3-36-3-3-20000000000000000001-211000
χ3566-3-36-3-3-36-3-200000000000000000011-21000
χ3666-3-3-36-3-3-36-2000000000000000000111-2000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1).