Finite Group Databasebeta

← Group #274161

Character table — Group #274161

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111-1-111-1-111
χ91111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ101111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-222-2-2222-2-2-2-22222-2-2-2-2-2-20000000022-2-2200000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-2-2-2-2-22222-2-200000000-2-222200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2222222-2-2-2-22200000000-2-222-200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-222-2-2-2-22222220000000022-2-2-200000000000000000000000000
χ2122222222-222-2-222-222-2-2-2-20000000022222222220000-2-2-2-2-20000000000000000000000
χ2222222222-222-2-222-222-2-2-2-20000000022-2-2-2-2-2-2-2-20000-222220000000000000000000000
χ2322222222-222-2-222-2-2-2-2-22200000000-2-22222-2-2-2-200002-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-2-2-22200000000-2-2-2-2-2-222220000222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222200000000-2-2000000000000-200002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222222200000000-2-2000000000000-20000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-20000000022000000000000200002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2000000002200000000000020000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292-22-2-2-22222-22-22-2-2002-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000000002-200002i−2i0000
χ302-22-2-2-22222-22-22-2-2002-2002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000-220000−2i2i0000
χ312-22-2-2-22222-22-22-2-2002-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000000002-20000−2i2i0000
χ322-22-2-2-22222-22-22-2-2002-200−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000-2200002i−2i0000
χ332-22-2-2-2222-222-2-22-200-22002i2i−2i−2i−2i−2i2i2i0000000000000000000000000002-2002i−2i00000000
χ342-22-2-2-2222-222-2-22-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000000-2200−2i2i00000000
χ352-22-2-2-2222-222-2-22-200-2200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000002-200−2i2i00000000
χ362-22-2-2-2222-222-2-22-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000-22002i−2i00000000
χ372-2-222-22-2200-2-200200002i−2i00002i−2i2i−2i2i−2i22−2−2i2i2−i2−i22-20002−2i2−i2i2−i2i2−i22−22−200000000000000
χ382-2-222-22-2200-2-200200002i−2i00002i−2i2i−2i2i−2i−2−222−i2−i2i2i22-2000−22−i2i2−i2i2−i2i2−22−2200000000000000
χ392-2-222-22-2200-2-200200002i−2i0000−2i2i−2i2i2i−2i22−2−2i2i2−i2−i2-220002−2i2−i2−i2i2−i2i2−22−2200000000000000
χ402-2-222-22-2200-2-200200002i−2i0000−2i2i−2i2i2i−2i−2−222−i2−i2i2i2-22000−22−i2i2i2−i2i2−i22−22−200000000000000
χ412-2-222-22-2200-2-20020000−2i2i00002i−2i2i−2i−2i2i22−2−2−i2−i2i2i2-220002−2−i2i2i2−i2i2−i2−22−2200000000000000
χ422-2-222-22-2200-2-20020000−2i2i00002i−2i2i−2i−2i2i−2−222i2i2−i2−i2-22000−22i2−i2−i2i2−i2i22−22−200000000000000
χ432-2-222-22-2200-2-20020000−2i2i0000−2i2i−2i2i−2i2i22−2−2−i2−i2i2i22-20002−2−i2i2−i2i2−i2i22−22−200000000000000
χ442-2-222-22-2200-2-20020000−2i2i0000−2i2i−2i2i−2i2i−2−222i2i2−i2−i22-2000−22i2−i2i2−i2i2−i2−22−2200000000000000
χ452-2-222-22-2-2002200-200002i−2i2-22-20000−2i2i22−2−2−i2−i2i2i2002i−2i0−22i2−i22−2−22−i2i2i2−i200000000000000
χ462-2-222-22-2-2002200-200002i−2i2-22-20000−2i2i−2−222i2i2−i2−i2002i−2i02−2−i2i2−222−2i2−i2−i2i200000000000000
χ472-2-222-22-2-2002200-200002i−2i-22-220000−2i2i22−2−2−i2−i2i2i200−2i2i0−22i2−i2−222−2i2−i2−i2i200000000000000
χ482-2-222-22-2-2002200-200002i−2i-22-220000−2i2i−2−222i2i2−i2−i200−2i2i02−2−i2i22−2−22−i2i2i2−i200000000000000
χ492-2-222-22-2-2002200-20000−2i2i2-22-200002i−2i22−2−2i2i2−i2−i200−2i2i0−22−i2i22−2−22i2−i2−i2i200000000000000
χ502-2-222-22-2-2002200-20000−2i2i2-22-200002i−2i−2−222−i2−i2i2i200−2i2i02−2i2−i2−222−2−i2i2i2−i200000000000000
χ512-2-222-22-2-2002200-20000−2i2i-22-2200002i−2i22−2−2i2i2−i2−i2002i−2i0−22−i2i2−222−2−i2i2i2−i200000000000000
χ522-2-222-22-2-2002200-20000−2i2i-22-2200002i−2i−2−222−i2−i2i2i2002i−2i02−2i2−i22−2−22i2−i2−i2i200000000000000
χ534444-4-4-4-4000000004-40000000000000022−2222−2222−2222−220000000000000000000000000000000
χ544444-4-4-4-4000000004-400000000000000−2222−2222−2222−22220000000000000000000000000000000
χ554444-4-4-4-400000000-440000000000000022−2222−22−2222−22220000000000000000000000000000000
χ564444-4-4-4-400000000-4400000000000000−2222−222222−2222−220000000000000000000000000000000
χ5744-4-44-4-4404-400-440000000000000000000000000000000000000000000000002i2−2i2000000
χ5844-4-44-4-4404-400-44000000000000000000000000000000000000000000000000−2i22i2000000
χ5944-4-44-4-440-44004-400000000000000000000000000000000000000000000000000002i2−2i200
χ6044-4-44-4-440-44004-40000000000000000000000000000000000000000000000000000−2i22i200
χ6144-4-4-444-4400-4400-400000000004-4-4400000000000000000000000000000000000000000
χ6244-4-4-444-4400-4400-40000000000-444-400000000000000000000000000000000000000000
χ6344-4-4-444-4-4004-40040000004i−4i−4i4i000000000000000000000000000000000000000000000
χ6444-4-4-444-4-4004-4004000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ654-44-4-4-444-44-4-444-4400-44000000000000000000000000000000000000000000000000000
χ664-44-4-4-444-4-44-44-444004-4000000000000000000000000000000000000000000000000000
χ674-4-44-44-4404400-4-40000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ684-4-44-44-4404400-4-4000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ694-4-44-44-440-4-40044000000000000000004-4-4400000000000000000000000000000000000
χ704-4-44-44-440-4-4004400000000000000000-444-400000000000000000000000000000000000
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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