Finite Group Databasebeta

← Group #98939

Character table — Group #98939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222222244444444444444448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i11ii−i−iii−i−i-1-1
χ1011111111-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii11−i−iii−i−iii-1-1
χ1111111111-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111ii−i−iii−i−i-1-1−i−iii−i−iii11
χ1211111111-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111−i−iii−i−iii-1-1ii−i−iii−i−i11
χ1311111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii-1-1ii−i−i−i−iii11
χ1411111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−i-1-1−i−iiiii−i−i11
χ1511111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iii11−i−iiiii−i−i-1-1
χ1611111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−i11ii−i−i−i−iii-1-1
χ17222222222222222-2-2-2-2222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222222-2-2-22222-2-2-222-2-2-2-200000000000000002-22-200000000000000000000
χ20222222222222-2-2-22222-2-2-222-2-2-2-20000000000000000-22-2200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000002i−2i000000002i−2i
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000−2i2i00000000−2i2i
χ2322222222-2-2-2-222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-222-2-200000000000000000000000000002i−2i00000000−2i2i
χ2622222222-2-2-2-2-2-2-22222-222-2-222-2-20000000000000000000000000000−2i2i000000002i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000002-2-2200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000-222-200000000000000000000
χ292222-2-2-2-222-2-222-20000-22-200000022-2-222-2-200000000000000000000002−22−22−22−200
χ302222-2-2-2-222-2-222-20000-22-200000022-2-222-2-20000000000000000000000−22−22−22−2200
χ312222-2-2-2-222-2-222-20000-22-2000000-2-222-2-22200000000000000000000002−22−2−22−2200
χ322222-2-2-2-222-2-222-20000-22-2000000-2-222-2-2220000000000000000000000−22−222−22−200
χ332222-2-2-2-2-2-22222-20000-2-2200000022-2-2-2-2220000000000000000000000i2−i2−i2i2i2−i2−i2i200
χ342222-2-2-2-2-2-22222-20000-2-2200000022-2-2-2-2220000000000000000000000−i2i2i2−i2−i2i2i2−i200
χ352222-2-2-2-2-2-22222-20000-2-22000000-2-22222-2-20000000000000000000000i2−i2−i2i2−i2i2i2−i200
χ362222-2-2-2-2-2-22222-20000-2-22000000-2-22222-2-20000000000000000000000−i2i2i2−i2i2−i2−i2i200
χ372-2-2222-2-20000-2222i2i−2i−2i-20000002i−2i2-22-2000000002i2i−2i−2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ382-2-2222-2-20000-2222i2i−2i−2i-20000002i−2i2-22-2000000002i2i−2i−2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ392-2-2222-2-20000-2222i2i−2i−2i-20000002i−2i-22-2200000000−2i−2i2i2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ402-2-2222-2-20000-2222i2i−2i−2i-20000002i−2i-22-2200000000−2i−2i2i2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ412-2-2222-2-20000-222−2i−2i2i2i-2000000−2i2i2-22-200000000−2i−2i2i2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ422-2-2222-2-20000-222−2i−2i2i2i-2000000−2i2i2-22-200000000−2i−2i2i2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ432-2-2222-2-20000-222−2i−2i2i2i-2000000−2i2i-22-22000000002i2i−2i−2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ442-2-2222-2-20000-222−2i−2i2i2i-2000000−2i2i-22-22000000002i2i−2i−2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ454444-4-4-4-444-4-4-4-4400004-440000000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-444-4-44000044-40000000000000000000000000000000000000000000000
χ4744-4-44-44-400000000000000004i−4i00000022−2222−2200002i2−2i22i2−2i2000000000000000000000000
χ4844-4-44-44-400000000000000004i−4i000000−2222−22220000−2i22i2−2i22i2000000000000000000000000
χ4944-4-44-44-40000000000000000−4i4i00000022−2222−220000−2i22i2−2i22i2000000000000000000000000
χ5044-4-44-44-40000000000000000−4i4i000000−2222−222200002i2−2i22i2−2i2000000000000000000000000
χ5144-4-4-44-4400000004i−4i4i−4i000000000000022−22−22222i22i2−2i2−2i20000000000000000000000000000
χ5244-4-4-44-4400000004i−4i4i−4i0000000000000−222222−22−2i2−2i22i22i20000000000000000000000000000
χ5344-4-4-44-440000000−4i4i−4i4i000000000000022−22−2222−2i2−2i22i22i20000000000000000000000000000
χ5444-4-4-44-440000000−4i4i−4i4i0000000000000−222222−222i22i2−2i2−2i20000000000000000000000000000
χ554-44-44-4-444-44-400000000000000000000000022−2222−2222−22−2222000000000000000000000000
χ564-44-44-4-444-44-4000000000000000000000000−2222−2222−222222−22000000000000000000000000
χ574-44-44-4-44-44-4400000000000000000000000022−2222−22−222222−22000000000000000000000000
χ584-44-44-4-44-44-44000000000000000000000000−2222−222222−22−2222000000000000000000000000
χ594-44-4-444-44-4-440004-4-440004-400000000000000000000000000000000000000000000
χ604-44-4-444-44-4-44000-444-4000-4400000000000000000000000000000000000000000000
χ614-44-4-444-4-444-40004-4-44000-4400000000000000000000000000000000000000000000
χ624-44-4-444-4-444-4000-444-40004-400000000000000000000000000000000000000000000
χ634-4-4444-4-400004-4-44i4i−4i−4i4000000−4i4i0000000000000000000000000000000000000000
χ644-4-4444-4-400004-4-4−4i−4i4i4i40000004i−4i0000000000000000000000000000000000000000
χ654-4-44-4-44400004-440000-400000000000000004i−4i−4i4i0000000000000000000000000000
χ664-4-44-4-44400004-440000-40000000000000000−4i4i4i−4i0000000000000000000000000000
χ674-4-44-4-4440000-44-400004000000004-4-44000000000000000000000000000000000000
χ684-4-44-4-4440000-44-40000400000000-444-4000000000000000000000000000000000000

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