Finite Group Databasebeta

← Group #93229

Character table — Group #93229

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11111111448888888888161616161616161616161616161616161616161616163232
order1222444424224444888844444444888888161616161616161624
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ51111111111-1-11-1-11-1-1-1-1iiii−i−i−i−i111111iiii−i−i−i−i-1-1
χ61111111111-1-11-1-11-1-1-1-1iiii−i−i−i−i11-1-1-1-1−i−i−i−iiiii11
χ71111111111-1-11-1-11-1-1-1-1−i−i−i−iiiii111111−i−i−i−iiiii-1-1
χ81111111111-1-11-1-11-1-1-1-1−i−i−i−iiiii11-1-1-1-1iiii−i−i−i−i11
χ92222222222222222-2-2-2-200000000-2-200000000000000
χ102222222222-2-22-2-22222200000000-2-200000000000000
χ112222-2-2-2-22-200200-22i2i−2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ122222-2-2-2-22-200200-22i2i−2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ132222-2-2-2-22-200200-2−2i−2i2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ142222-2-2-2-22-200200-2−2i−2i2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ152222-2-2-2-22-222-2-2-2200000000000000000022−2−222−2−200
χ162222-2-2-2-22-222-2-2-22000000000000000000−2−222−2−22200
χ172222-2-2-2-22-2-2-2-2222000000000000000000i2i2−i2−i2−i2−i2i2i200
χ182222-2-2-2-22-2-2-2-2222000000000000000000−i2−i2i2i2i2i2−i2−i200
χ19444444444400-400-40000000000000000000000000000
χ2044444444-4-40000000000000000000022-2-20000000000
χ2144444444-4-400000000000000000000-2-2220000000000
χ224444-4-4-4-4-44000000000000000000000000000000002-2
χ234444-4-4-4-4-4400000000000000000000000000000000-22
χ2444-4-44i−4i4i−4i000000002ζ2−2ζ22ζ6−2ζ600000000000000ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ500
χ2544-4-44i−4i4i−4i000000002ζ2−2ζ22ζ6−2ζ600000000000000−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ500
χ2644-4-44i−4i4i−4i00000000−2ζ22ζ2−2ζ62ζ600000000000000ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ500
χ2744-4-44i−4i4i−4i00000000−2ζ22ζ2−2ζ62ζ600000000000000−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ500
χ2844-4-4−4i4i−4i4i000000002ζ6−2ζ62ζ2−2ζ200000000000000ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ700
χ2944-4-4−4i4i−4i4i000000002ζ6−2ζ62ζ2−2ζ200000000000000−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ700
χ3044-4-4−4i4i−4i4i00000000−2ζ62ζ6−2ζ22ζ200000000000000ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ700
χ3144-4-4−4i4i−4i4i00000000−2ζ62ζ6−2ζ22ζ200000000000000−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ700
χ324-44-44i−4i−4i4i002-202i−2i000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ334-44-44i−4i−4i4i002-202i−2i00000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ344-44-44i−4i−4i4i00-220−2i2i000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000000000
χ354-44-44i−4i−4i4i00-220−2i2i00000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000000000
χ364-44-4−4i4i4i−4i002-20−2i2i000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ374-44-4−4i4i4i−4i002-20−2i2i00000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ384-44-4−4i4i4i−4i00-2202i−2i000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000000000
χ394-44-4−4i4i4i−4i00-2202i−2i00000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000000000
χ404-4-44-4-444000000000000000000002-20022−220000000000
χ414-4-44-4-444000000000000000000002-200−22220000000000
χ424-4-44-4-44400000000000000000000-2222−22000000000000
χ434-4-44-4-44400000000000000000000-22−2222000000000000
χ448-8-8888-8-8000000000000000000000000000000000000

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