Finite Group Databasebeta

← Group #1348

Character table — Group #1348

Order 128.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29
size1111222222224444444444488881616
order1222224488884881616161616161616444444
χ111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-1
χ3111111111111111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-111-1-1-1-1-111iiii−i−i−i−iii−i−i1-1
χ61111-1-111-1-1-1-1-111iiii−i−i−i−i−i−iii-11
χ71111-1-111-1-1-1-1-111−i−i−i−iiiiiii−i−i-11
χ81111-1-111-1-1-1-1-111−i−i−i−iiiii−i−iii1-1
χ922222222-2-2-2-22-2-200000000000000
χ10222222-2-20000-20022−2−222−2−2000000
χ11222222-2-20000-200−2−222−2−222000000
χ122222-2-2222222-2-2-200000000000000
χ132222-2-2-2-20000200i2i2−i2−i2−i2−i2i2i2000000
χ142222-2-2-2-20000200−i2−i2i2i2i2i2−i2−i2000000
χ1522-2-22-20022−2−202−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000
χ1622-2-22-20022−2−202−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000
χ1722-2-22-200−2−2220−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000
χ1822-2-22-200−2−2220−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000
χ1922-2-2-220022−2−20−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000
χ2022-2-2-220022−2−20−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000
χ2122-2-2-2200−2−22202−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000
χ2222-2-2-2200−2−22202−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000
χ232-2-22002-22i−2i2i−2i000000000001−i−1+i1+i−1−i00
χ242-2-22002-22i−2i2i−2i00000000000−1+i1−i−1−i1+i00
χ252-2-22002-2−2i2i−2i2i000000000001+i−1−i1−i−1+i00
χ262-2-22002-2−2i2i−2i2i00000000000−1−i1+i−1+i1−i00
χ274-44-400002i2−2i2−2i22i200000000000000000
χ284-44-40000−2i22i22i2−2i200000000000000000
χ294-4-4400-44000000000000000000000

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