Finite Group Databasebeta

← Group #150201

Character table — Group #150201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224422444444444422448888888888888888224444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-1-1-1-1-11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1iiii−i−i−i−i
χ6111111111111111-1-1-1-1-1-1-1-11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111−i−i−i−iiiii
χ7111111111111111-1-1-1-1-1-1-1-11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1−i−i−i−iiiii
χ8111111111111111-1-1-1-1-1-1-1-11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111iiii−i−i−i−i
χ91111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-11-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-11-1-111ii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-11-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-111111-11-11-1-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-11-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1111-1-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-11-1-1-1-111111-1-111-1-1-1-111111111-1-1-1-11-11-11-1-1-111-1-11111-1-1
χ161111-1-1-1-111-1-1-1-11-1-1-1-111111-1-111-1-1-1-111111111-1-1-1-1-111-1-1111-1-111-1-1-1-111
χ17222222222222222222222222-2-2-2-2000000000000000000-2-200000000000000
χ18222222222222222-2-2-2-2-2-2-2-222222000000000000000000-2-200000000000000
χ192222-2-2-2-222-2-2-2-222222-2-2-2-22-2-222000000000000000000-2200000000000000
χ202222-2-2-2-222-2-2-2-22-2-2-2-22222222-2-2000000000000000000-2200000000000000
χ212-2-2222-2-22-22-22-222i2i−2i−2i2i2i−2i−2i-20000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ222-2-2222-2-22-22-22-222i2i−2i−2i2i2i−2i−2i-2000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ232-2-2222-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i-20000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ242-2-2222-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i-2000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ252-2-2222-2-22-22-2-22-20000000022-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000
χ262-2-2222-2-22-22-2-22-20000000022-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000
χ272-2-2222-2-22-22-2-22-2000000002-22-2222−2−222−2−2−2−222−2−222000000000000000000
χ282-2-2222-2-22-22-2-22-2000000002-22-22−2−222−2−22222−2−222−2−2000000000000000000
χ292-2-22-2-2222-2-222-2-20000000022-2-2222−2−2−2−22222−2−2−2−222000000000000000000
χ302-2-22-2-2222-2-222-2-20000000022-2-22−2−22222−2−2−2−22222−2−2000000000000000000
χ312-2-22-2-2222-2-222-2-2000000002-222-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ322-2-22-2-2222-2-222-2-2000000002-222-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ332-2-22-2-2222-2-22-2222i2i−2i−2i−2i−2i2i2i-20000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ342-2-22-2-2222-2-22-2222i2i−2i−2i−2i−2i2i2i-2000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ352-2-22-2-2222-2-22-222−2i−2i2i2i2i2i−2i−2i-20000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ362-2-22-2-2222-2-22-222−2i−2i2i2i2i2i−2i−2i-2000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ37444444444444-4-4-400000000-400000000000000000000000000000000000000
χ3844444444-4-4-4-4000000000000000000000000000000002-200-22000000000000
χ3944444444-4-4-4-400000000000000000000000000000000-22002-2000000000000
χ404444-4-4-4-444-4-444-400000000-400000000000000000000000000000000000000
χ414444-4-4-4-4-4-444000000000000000000000000000000002200-2-2000000000000
χ424444-4-4-4-4-4-44400000000000000000000000000000000-2-20022000000000000
χ4344-4-44i−4i4i−4i00000002-22-22i−2i2i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ4444-4-44i−4i4i−4i00000002-22-22i−2i2i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ4544-4-44i−4i4i−4i0000000-22-22−2i2i−2i2i000001−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i000000000000000000
χ4644-4-44i−4i4i−4i0000000-22-22−2i2i−2i2i00000−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i000000000000000000
χ4744-4-4−4i4i−4i4i00000002-22-2−2i2i−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4844-4-4−4i4i−4i4i00000002-22-2−2i2i−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4944-4-4−4i4i−4i4i0000000-22-222i−2i2i−2i000001+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000000000
χ5044-4-4−4i4i−4i4i0000000-22-222i−2i2i−2i00000−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i000000000000000000
χ514-44-44i−4i−4i4i00000002i−2i−2i2i-222-2000002−2−22−i2i2i2−i2−i2i2i2−i2−222−2000000000000000000
χ524-44-44i−4i−4i4i00000002i−2i−2i2i-222-200000−222−2i2−i2−i2i2i2−i2−i2i22−2−22000000000000000000
χ534-44-44i−4i−4i4i0000000−2i2i2i−2i2-2-2200000i2−i2−i2i22−2−22−222−2i2−i2−i2i2000000000000000000
χ544-44-44i−4i−4i4i0000000−2i2i2i−2i2-2-2200000−i2i2i2−i2−222−22−2−22−i2i2i2−i2000000000000000000
χ554-44-4−4i4i4i−4i00000002i−2i−2i2i2-2-2200000i2−i2−i2i2−222−22−2−22i2−i2−i2i2000000000000000000
χ564-44-4−4i4i4i−4i00000002i−2i−2i2i2-2-2200000−i2i2i2−i22−2−22−222−2−i2i2i2−i2000000000000000000
χ574-44-4−4i4i4i−4i0000000−2i2i2i−2i-222-2000002−2−22i2−i2−i2i2i2−i2−i2i2−222−2000000000000000000
χ584-44-4−4i4i4i−4i0000000−2i2i2i−2i-222-200000−222−2−i2i2i2−i2−i2i2i2−i22−2−22000000000000000000
χ594-4-4444-4-4-44-44000000000000000000000000000000000000002-22-200000000
χ604-4-4444-4-4-44-4400000000000000000000000000000000000000-22-2200000000
χ614-4-44-4-444-444-4000000000000000000000000000000000000002-2-2200000000
χ624-4-44-4-444-444-400000000000000000000000000000000000000-222-200000000

Here i is the imaginary unit (i² = −1).