Finite Group Databasebeta

← Group #344006

Character table — Group #344006

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-111-1-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-111111-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-111-1-111-1-1-1-11-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1111111-11
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-11-1-111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-11111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-11-1-1-1-1-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111-1-1-1-1-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-11111111-1-111-1-1-1-1
χ17222222222-2-22-222-2-2-222220000-2-2-2-20000000000000022-2-20000-2200000000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-200000000000000-2-22200002-200000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-2000022220000000000000022220000-2-200000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-20000222200000000000000-2-2-2-200002200000000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-20000000022000022-2-20000000000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-200000000-2-20000-2-2220000000000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-20000222200000000220000-2-2-220000000000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-20000222200000000-2-20000222-20000000000000000
χ2522-22-2-2-222-2-2-222-222-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000002i−2i2-20000000000
χ2622-22-2-2-222-2-2-222-222-200000000000000002i2i2i2i−2i−2i−2i−2i000000000000−2i2i-220000000000
χ2722-22-2-2-222-2-2-222-222-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000002i−2i-220000000000
χ2822-22-2-2-222-2-2-222-222-20000000000000000−2i−2i−2i−2i2i2i2i2i000000000000−2i2i2-20000000000
χ292-222-22-2-2-200-2022000000022−2−222-2-222−2−222−2−222−2−2002i−2i2i−2i00000000000000i2−i2i2−i200
χ302-222-22-2-2-200-2022000000022−2−222-2-222−2−222−2−222−2−200−2i2i−2i2i00000000000000−i2i2−i2i200
χ312-222-22-2-2-200-2022000000022−2−2-2-22222−2−2−2−222−2−222002i−2i−2i2i00000000000000i2−i2−i2i200
χ322-222-22-2-2-200-2022000000022−2−2-2-22222−2−2−2−222−2−22200−2i2i2i−2i00000000000000−i2i2i2−i200
χ332-222-22-2-2-200-20220000000−2−22222-2-2−2−222−2−222−2−222002i−2i2i−2i00000000000000−i2i2−i2i200
χ342-222-22-2-2-200-20220000000−2−22222-2-2−2−222−2−222−2−22200−2i2i−2i2i00000000000000i2−i2i2−i200
χ352-222-22-2-2-200-20220000000−2−222-2-222−2−22222−2−222−2−2002i−2i−2i2i00000000000000−i2i2i2−i200
χ362-222-22-2-2-200-20220000000−2−222-2-222−2−22222−2−222−2−200−2i2i2i−2i00000000000000i2−i2−i2i200
χ372-22-2-2-22202-20200-20022−2−22-22-22−22−200002−22−22−22−22i−2i00002i−2i00000000i2−i2i2−i2000000
χ382-22-2-2-22202-20200-20022−2−22-22-22−22−200002−22−22−22−2−2i2i0000−2i2i00000000−i2i2−i2i2000000
χ392-22-2-2-22202-20200-20022−2−2-22-222−22−20000−22−22−22−222i−2i0000−2i2i00000000i2−i2−i2i2000000
χ402-22-2-2-22202-20200-20022−2−2-22-222−22−20000−22−22−22−22−2i2i00002i−2i00000000−i2i2i2−i2000000
χ412-22-2-2-22202-20200-200−2−2222-22-2−22−220000−22−22−22−222i−2i00002i−2i00000000−i2i2−i2i2000000
χ422-22-2-2-22202-20200-200−2−2222-22-2−22−220000−22−22−22−22−2i2i0000−2i2i00000000i2−i2i2−i2000000
χ432-22-2-2-22202-20200-200−2−222-22-22−22−2200002−22−22−22−22i−2i0000−2i2i00000000−i2i2i2−i2000000
χ442-22-2-2-22202-20200-200−2−222-22-22−22−2200002−22−22−22−2−2i2i00002i−2i00000000i2−i2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-40000000000000022−22−222222−22−222200002-2-222-2-2200000000000000000000000000
χ47444-44-4-4-40000000000000022−22−2222−222222−220000-222-2-222-200000000000000000000000000
χ48444-44-4-4-400000000000000−222222−2222−22−22220000-222-2-222-200000000000000000000000000
χ49444-44-4-4-400000000000000−222222−22−222222−2200002-2-222-2-2200000000000000000000000000
χ5044-44-4-4-44444-4-44-4-4-4400000000000000000000000000000000000000000000000000
χ5144-44-4-4-44-4444-4-44-44-400000000000000000000000000000000000000000000000000
χ5244-44-4-4-44-4-4-444-444-4400000000000000000000000000000000000000000000000000
χ5344-4-4-444-400000000002i2−2i22i2−2i20000000022−2222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5444-4-4-444-400000000002i2−2i22i2−2i200000000−2222−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-4-444-40000000000−2i22i2−2i22i20000000022−2222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5644-4-4-444-40000000000−2i22i2−2i22i200000000−2222−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ574-444-44-4-440040-4-400000002222−22−220000−22−2222220000000000000000000000000000000000
χ584-444-44-4-440040-4-40000000−22−22222200002222−22−220000000000000000000000000000000000
χ594-44-4-4-4440-440-4004002222−22−220000−2222−222200000000000000000000000000000000000000
χ604-44-4-4-4440-440-400400−22−222222000022−2222−2200000000000000000000000000000000000000
χ614-4-444-44-4400-40-440004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-4-444-44-4400-40-44000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-4-444-44-4-400404-400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ644-4-444-44-4-400404-40000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ654-4-4-444-4404-40-4004000000000000004-4-440000000000000000000000000000000000
χ664-4-4-444-4404-40-400400000000000000-444-40000000000000000000000000000000000
χ674-4-4-444-440-440400-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ684-4-4-444-440-440400-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000

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