Finite Group Databasebeta

← Group #342123

Character table — Group #342123

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822224444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-11-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-1-1-1-11-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-1-1-111-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111-11-1-1-1-1-1-1111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1111111-1-11-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111-1-1-11111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-11111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-111-1-1-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-11111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1-1-11-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-1-11-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1
χ17222222222-222-2-2-22-2-22222-2-2-2-2000000000000000022002200000-2000-20000000000
χ18222222222-222-2-2-22-2-22222-2-2-2-20000000000000000-2-200-2-200000200020000000000
χ19222222222-222-2-2-22-2-2-2-2-2-2222200000000000000002200-2-2000002000-20000000000
χ20222222222-222-2-2-22-2-2-2-2-2-222220000000000000000-2-2002200000-200020000000000
χ2122222222-22-2-2222-2-2-2000000002222-2-2-2-200000000002200-2-2200000-200000000000
χ2222222222-22-2-2222-2-2-2000000002222-2-2-2-20000000000-2-20022-200000200000000000
χ2322222222-22-2-2222-2-2-200000000-2-2-2-222220000000000220022-200000-200000000000
χ2422222222-22-2-2222-2-2-200000000-2-2-2-222220000000000-2-200-2-2200000200000000000
χ2522-2-2-2-222-2222-22-2-22-200000000000000002i2i2i2i−2i−2i−2i−2i0000000002-202i−2i000000000000
χ2622-2-2-2-222-2222-22-2-22-200000000000000002i2i2i2i−2i−2i−2i−2i000000000-220−2i2i000000000000
χ2722-2-2-2-222-2222-22-2-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000002-20−2i2i000000000000
χ2822-2-2-2-222-2222-22-2-22-20000000000000000−2i−2i−2i−2i2i2i2i2i000000000-2202i−2i000000000000
χ292-222-2-2-2202002-2-200022−2−222−2−200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2002-2002i−2i0000000000002−2i2−i200
χ302-222-2-2-2202002-2-200022−2−222−2−200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i200-2200−2i2i000000000000−22−i2i200
χ312-222-2-2-2202002-2-200022−2−222−2−20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2002-200−2i2i0000000000002−2−i2i200
χ322-222-2-2-2202002-2-200022−2−222−2−20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i200-22002i−2i000000000000−22i2−i200
χ332-222-2-2-2202002-2-2000−2−222−2−22200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2002-2002i−2i000000000000−22−i2i200
χ342-222-2-2-2202002-2-2000−2−222−2−22200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i200-2200−2i2i0000000000002−2i2−i200
χ352-222-2-2-2202002-2-2000−2−222−2−2220000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2002-200−2i2i000000000000−22i2−i200
χ362-222-2-2-2202002-2-2000−2−222−2−2220000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i200-22002i−2i0000000000002−2−i2i200
χ372-22-22-22-2202-2000-2002i−2i2i−2i000022−2−22−22−2i2−i2i2−i2i2−i2i2−i22-2002i−2i00000000002−2i2−i2000000
χ382-22-22-22-2202-2000-2002i−2i2i−2i000022−2−22−22−2i2−i2i2−i2i2−i2i2−i2-2200−2i2i0000000000−22−i2i2000000
χ392-22-22-22-2202-2000-2002i−2i2i−2i0000−2−222−22−22−i2i2−i2i2−i2i2−i2i22-2002i−2i0000000000−22−i2i2000000
χ402-22-22-22-2202-2000-2002i−2i2i−2i0000−2−222−22−22−i2i2−i2i2−i2i2−i2i2-2200−2i2i00000000002−2i2−i2000000
χ412-22-22-22-2202-2000-200−2i2i−2i2i000022−2−22−22−2−i2i2−i2i2−i2i2−i2i22-200−2i2i00000000002−2−i2i2000000
χ422-22-22-22-2202-2000-200−2i2i−2i2i000022−2−22−22−2−i2i2−i2i2−i2i2−i2i2-22002i−2i0000000000−22i2−i2000000
χ432-22-22-22-2202-2000-200−2i2i−2i2i0000−2−222−22−22i2−i2i2−i2i2−i2i2−i22-200−2i2i0000000000−22i2−i2000000
χ442-22-22-22-2202-2000-200−2i2i−2i2i0000−2−222−22−22i2−i2i2−i2i2−i2i2−i2-22002i−2i00000000002−2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i2-222-2-222-200000000000000000000000000
χ47444-4-44-4-400000000002i2−2i2−2i22i200000000−2i22i22i2−2i22-2-222-2-2200000000000000000000000000
χ48444-4-44-4-40000000000−2i22i22i2−2i2000000002i2−2i2−2i22i22-2-222-2-2200000000000000000000000000
χ49444-4-44-4-40000000000−2i22i22i2−2i200000000−2i22i22i2−2i2-222-2-222-200000000000000000000000000
χ5044-444-4-4-4000000000000002i2−2i22i2−2i222−2222−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5144-444-4-4-4000000000000002i2−2i22i2−2i2−2222−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5244-444-4-4-400000000000000−2i22i2−2i22i222−2222−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5344-444-4-4-400000000000000−2i22i2−2i22i2−2222−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5444-4-4-4-44444-4-4-44-44-4400000000000000000000000000000000000000000000000000
χ5544-4-4-4-4444-4-4-44-4444-400000000000000000000000000000000000000000000000000
χ5644-4-4-4-444-4-4444-44-4-4400000000000000000000000000000000000000000000000000
χ574-444-4-4-440-400-4440002222−22−22−22−222222000000000000000000000000000000000000000000
χ584-444-4-4-440-400-444000−22−2222222222−22−22000000000000000000000000000000000000000000
χ594-44-44-44-4-40-44000400000000002222−22−22−2222−22220000000000000000000000000000000000
χ604-44-44-44-4-40-4400040000000000−22−22222222−2222−220000000000000000000000000000000000
χ614-4-44-444-440-44000-40000004i−4i−4i4i000000000000000000000000000000000000000000
χ624-4-44-444-440-44000-4000000−4i4i4i−4i000000000000000000000000000000000000000000
χ634-4-44-444-4-404-4000400000000000000000022−2222−22−2222−222200000000000000000000000000
χ644-4-44-444-4-404-40004000000000000000000−2222−222222−2222−2200000000000000000000000000
χ654-4-4-444-440400-4-4400000000000000000002222−22−22−22−22222200000000000000000000000000
χ664-4-4-444-440400-4-440000000000000000000−22−2222222222−22−2200000000000000000000000000
χ674-4-4-444-440-40044-4000000000004-4-4400000000000000000000000000000000000000
χ684-4-4-444-440-40044-400000000000-444-400000000000000000000000000000000000000

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