Finite Group Databasebeta

← Group #12331

Character table — Group #12331

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222224444444444444888888888161616161632
order1222444488884448816161616161616164448816161616244882
χ11111111111111111111111111111111111111111
χ211111111111111111111111111-1-1111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1
χ411111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1111
χ51111111111111-1-11111111111-111-1-1-1-1-1-11-1-111-1
χ61111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11
χ71111111111111-1-111-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-11
χ81111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1
χ922222222-2-2-2-2222-2-200000000200-2-20000000000
χ1022222222-2-2-2-22-2-2-2-200000000-200220000000000
χ1122222-2-220000-222002222−2−2−2−2-2000022−2−2000000
χ1222222-2-220000-22200−2−2−2−22222-20000−2−222000000
χ1322222-2-220000-2-2-2002222−2−2−2−220000−2−222000000
χ1422222-2-220000-2-2-200−2−2−2−222222000022−2−2000000
χ152222-222-22222-200-2-200000000022000000-200000
χ162222-222-22222-200-2-2000000000-2-2000000200000
χ172222-222-2-2-2-2-2-200220000000000000000002-2000
χ182222-222-2-2-2-2-2-20022000000000000000000-22000
χ192-22-2200-22−22−202i−2i2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000
χ202-22-2200-22−22−202i−2i2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000
χ212-22-2200-22−22−20−2i2i2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000
χ222-22-2200-22−22−20−2i2i2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000
χ232-22-2200-2−22−2202i−2i−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000
χ242-22-2200-2−22−2202i−2i−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000
χ252-22-2200-2−22−220−2i2i−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000
χ262-22-2200-2−22−220−2i2i−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000
χ272-2-2202-2022-2-2000002−22−22−22−202i−2i000000000i2−i20
χ282-2-2202-2022-2-2000002−22−22−22−20−2i2i000000000−i2i20
χ292-2-2202-2022-2-200000−22−22−22−2202i−2i000000000−i2i20
χ302-2-2202-2022-2-200000−22−22−22−220−2i2i000000000i2−i20
χ314444-4-4-4-400004000000000000000000000000000
χ3244-4-4000022−22−222200000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ3344-4-4000022−22−222200000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ3444-4-40000−222222−2200000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ3544-4-40000−222222−2200000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ364-44-4-400422−2222−22000−222200000000000000000000000
χ374-44-4-4004−2222−222200022−2200000000000000000000000
χ384-4-4404-40-4-4440000000000000000000000000000
χ394-4-440-4400000000002-22-2-22-22000000000000000
χ404-4-440-440000000000-22-222-22-2000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.