Finite Group Databasebeta

← Group #98971

Character table — Group #98971

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ9111111111-1-111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i-1-1ii−i−iii−i−i
χ10111111111-1-111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iii-1-1−i−iii−i−iii
χ11111111111-1-111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1ii−i−iii−i−i11−i−iii−i−iii
χ12111111111-1-111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1−i−iii−i−iii11ii−i−iii−i−i
χ13111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1ii−i−i−i−iii11ii−i−i−i−iii
χ14111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i11−i−iiiii−i−i
χ15111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111ii−i−i−i−iii-1-1−i−iiiii−i−i
χ16111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111−i−iiiii−i−i-1-1ii−i−i−i−iii
χ172222222222222-2-2-2-222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222-2-22222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ20222222222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2122222222-222-2-22222-222-2-222-2-2-2-200000000000000002-22-200000000000000000000
χ2222222222-222-2-22222-222-2-222-2-2-2-20000000000000000-22-2200000000000000000000
χ2322222222-222-2-2-2-2-2-2-222-2-2-2-22222000000000000000000002i−2i000000002i−2i00000000
χ2422222222-222-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000−2i2i00000000−2i2i00000000
χ2522222222-2-2-2-2-22222-2-2-222-2-222-2-2000000000000000000002i−2i00000000−2i2i00000000
χ2622222222-2-2-2-2-22222-2-2-222-2-222-2-200000000000000000000−2i2i000000002i−2i00000000
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
χ292222-2-2-2-22222-20000-2-2-22-200000022-2-222-2-2000000000000002−22−22−22−20000000000
χ302222-2-2-2-22222-20000-2-2-22-200000022-2-222-2-200000000000000−22−22−22−220000000000
χ312222-2-2-2-22222-20000-2-2-22-2000000-2-222-2-222000000000000002−22−2−22−220000000000
χ322222-2-2-2-22222-20000-2-2-22-2000000-2-222-2-22200000000000000−22−222−22−20000000000
χ332222-2-2-2-22-2-22-20000-222-2200000022-2-2-2-22200000000000000i2−i2−i2i2i2−i2−i2i20000000000
χ342222-2-2-2-22-2-22-20000-222-2200000022-2-2-2-22200000000000000−i2i2i2−i2−i2i2i2−i20000000000
χ352222-2-2-2-22-2-22-20000-222-22000000-2-22222-2-200000000000000i2−i2−i2i2−i2i2i2−i20000000000
χ362222-2-2-2-22-2-22-20000-222-22000000-2-22222-2-200000000000000−i2i2i2−i2i2−i2−i2i20000000000
χ372-2-2222-2-2-200222i2i−2i−2i-2000000002i−2i2-22-2000000002i2i−2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ382-2-2222-2-2-200222i2i−2i−2i-2000000002i−2i2-22-2000000002i2i−2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ392-2-2222-2-2-200222i2i−2i−2i-2000000002i−2i-22-2200000000−2i−2i2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ402-2-2222-2-2-200222i2i−2i−2i-2000000002i−2i-22-2200000000−2i−2i2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ412-2-2222-2-2-20022−2i−2i2i2i-200000000−2i2i2-22-200000000−2i−2i2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ422-2-2222-2-2-20022−2i−2i2i2i-200000000−2i2i2-22-200000000−2i−2i2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ432-2-2222-2-2-20022−2i−2i2i2i-200000000−2i2i-22-22000000002i2i−2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ442-2-2222-2-2-20022−2i−2i2i2i-200000000−2i2i-22-22000000002i2i−2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ454444-4-4-4-4-444-4400004-4-4-440000000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4-4-4400004444-40000000000000000000000000000000000000000000000
χ4744-4-44-44-400000000000000004i−4i0000002i2−2i22i2−2i2000022−2222−22000000000000000000000000
χ4844-4-44-44-400000000000000004i−4i000000−2i22i2−2i22i20000−2222−2222000000000000000000000000
χ4944-4-44-44-40000000000000000−4i4i0000002i2−2i22i2−2i20000−2222−2222000000000000000000000000
χ5044-4-44-44-40000000000000000−4i4i000000−2i22i2−2i22i2000022−2222−22000000000000000000000000
χ5144-4-4-44-44000004-44-40000000000000002i2−2i2−2i22i22i22i2−2i2−2i20000000000000000000000000000
χ5244-4-4-44-44000004-44-4000000000000000−2i22i22i2−2i2−2i2−2i22i22i20000000000000000000000000000
χ5344-4-4-44-4400000-44-440000000000000002i2−2i2−2i22i2−2i2−2i22i22i20000000000000000000000000000
χ5444-4-4-44-4400000-44-44000000000000000−2i22i22i2−2i22i22i2−2i2−2i20000000000000000000000000000
χ554-44-44-4-4404i−4i00000004i−4i000000000000000022−2222−222i2−2i2−2i22i2000000000000000000000000
χ564-44-44-4-4404i−4i00000004i−4i0000000000000000−2222−2222−2i22i22i2−2i2000000000000000000000000
χ574-44-44-4-440−4i4i0000000−4i4i000000000000000022−2222−22−2i22i22i2−2i2000000000000000000000000
χ584-44-44-4-440−4i4i0000000−4i4i0000000000000000−2222−22222i2−2i2−2i22i2000000000000000000000000
χ594-44-4-444-404i−4i004i−4i−4i4i0−4i4i004-400000000000000000000000000000000000000000000
χ604-44-4-444-404i−4i00−4i4i4i−4i0−4i4i00-4400000000000000000000000000000000000000000000
χ614-44-4-444-40−4i4i004i−4i−4i4i04i−4i00-4400000000000000000000000000000000000000000000
χ624-44-4-444-40−4i4i00−4i4i4i−4i04i−4i004-400000000000000000000000000000000000000000000
χ634-4-4444-4-4400-4-44i4i−4i−4i400000000−4i4i0000000000000000000000000000000000000000
χ644-4-4444-4-4400-4-4−4i−4i4i4i4000000004i−4i0000000000000000000000000000000000000000
χ654-4-44-4-444400-440000-40000000000000000004i−4i−4i4i0000000000000000000000000000
χ664-4-44-4-444400-440000-4000000000000000000−4i4i4i−4i0000000000000000000000000000
χ674-4-44-4-444-4004-40000400000000004-4-44000000000000000000000000000000000000
χ684-4-44-4-444-4004-4000040000000000-444-4000000000000000000000000000000000000

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