Finite Group Databasebeta

← Group #101129

Character table — Group #101129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2222222-2-222-2-200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-22-2000000002-22-200000000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-22222-2-22-2000000002-22-2000000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-2-2-2200000000-22-22000022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2200000000-22-220000-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2000000002-2-2200002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222-2000000002-2-220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2200000000-222-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2200000000-222-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-22-2-22-22-22i2i−2i−2i2i−2i0022-2-22i2i−2i−2i000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ30222-2-22-2-22-22-22i2i−2i−2i2i−2i0022-2-22i2i−2i−2i00000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ31222-2-22-2-22-22-22i2i−2i−2i2i−2i00-2-222−2i−2i2i2i000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ32222-2-22-2-22-22-22i2i−2i−2i2i−2i00-2-222−2i−2i2i2i00000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ33222-2-22-2-22-22-2−2i−2i2i2i−2i2i0022-2-2−2i−2i2i2i000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ34222-2-22-2-22-22-2−2i−2i2i2i−2i2i0022-2-2−2i−2i2i2i00000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ35222-2-22-2-22-22-2−2i−2i2i2i−2i2i00-2-2222i2i−2i−2i000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ36222-2-22-2-22-22-2−2i−2i2i2i−2i2i00-2-2222i2i−2i−2i00000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ372-22-2-2-22222-2-20000002-22i−2i2i−2i0000-2200002i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-22-2-2-22222-2-20000002-22i−2i2i−2i0000-2200002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-22-2-2-22222-2-20000002-2−2i2i−2i2i0000-220000−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-22-2-2-22222-2-20000002-2−2i2i−2i2i0000-220000−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-22-2-2-22222-2-2000000-222i−2i2i−2i00002-20000−2i2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ422-22-2-2-22222-2-2000000-222i−2i2i−2i00002-20000−2i2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ432-22-2-2-22222-2-2000000-22−2i2i−2i2i00002-200002i−2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ442-22-2-2-22222-2-2000000-22−2i2i−2i2i00002-200002i−2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ452-22-2-2-222-2-2220000002200002-22-2-2-2002-200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ462-22-2-2-222-2-2220000002200002-22-2-2-2002-200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ472-22-2-2-222-2-222000000220000-22-22-2-200-2200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ482-22-2-2-222-2-222000000220000-22-22-2-200-2200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ492-22-2-2-222-2-222000000-2-200002-22-22200-22002−2−222−2−22−222−22−2−220000000000000000
χ502-22-2-2-222-2-222000000-2-200002-22-22200-2200−222−2−222−22−2−22−222−20000000000000000
χ512-22-2-2-222-2-222000000-2-20000-22-2222002-2002−2−222−2−222−2−22−222−20000000000000000
χ522-22-2-2-222-2-222000000-2-20000-22-2222002-200−222−2−222−2−222−22−2−220000000000000000
χ53444-4-44-4-4-44-444i4i−4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-44-44−4i−4i4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5544-44-4-44-400004-44-400000000000000000000000000000000000000002i−2i2i−2i00000000
χ5644-44-4-44-400004-44-40000000000000000000000000000000000000000−2i2i−2i2i00000000
χ5744-44-4-44-40000-44-4400000000000000000000000000000000000000002i−2i−2i2i00000000
χ5844-44-4-44-40000-44-440000000000000000000000000000000000000000−2i2i2i−2i00000000
χ5944-4-44-4-4400004i−4i−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ6044-4-44-4-4400004i−4i−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ6144-4-44-4-440000−4i4i4i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ6244-4-44-4-440000−4i4i4i−4i000000000000000000000000000000000000-222i−2i000000000000
χ634-4444-4-4-44-4-44000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ644-4444-4-4-44-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ654-4444-4-4-4-444-40000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ664-4444-4-4-4-444-4000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ678-8-88-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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