Finite Group Databasebeta

← Group #10589488

Character table — Group #10589488

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size11112222222222668888888888888888888888881212121212363636367272
order12223446661212121244999181818181818181818363636363636363636363636412121212888844
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ311111-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1
χ411111-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11
χ52222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222000000
χ622222-2-2222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1111111111111-222-2-2000000
χ72222-122-1-1-1-1-1-1-122ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ682-1-1-1-1000000
χ82222-122-1-1-1-1-1-1-122ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ682-1-1-1-1000000
χ92222-122-1-1-1-1-1-1-122−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4−ζ44+ζ522-1-1-1-1000000
χ102222-1-2-2-1-1-1111122ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68-2-1-111000000
χ112222-1-2-2-1-1-1111122ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68-2-1-111000000
χ122222-1-2-2-1-1-1111122−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68ζ4+ζ68ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52-2-1-111000000
χ1322-2-2200-22-200002-22222-22-22-2-2-2-200000000000002-200000000
χ1422-2-2200-22-200002-2-1-1-1-11-11-1111133−3−333−3−333−3−302-200000000
χ1522-2-2200-22-200002-2-1-1-1-11-11-11111−3−333−3−333−3−33302-200000000
χ1622-2-2-1001-1133−3−32-2ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ14+ζ62+ζ70ζ14+ζ62+ζ70−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ14+ζ22−ζ14+ζ22ζ14−ζ22ζ14−ζ220-113−3000000
χ1722-2-2-1001-1133−3−32-2ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ14+ζ22−ζ14+ζ22ζ14−ζ22ζ14−ζ22ζ14+ζ62+ζ70ζ14+ζ62+ζ70−ζ14−ζ62−ζ70−ζ14−ζ62−ζ700-113−3000000
χ1822-2-2-1001-1133−3−32-2−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ14+ζ22−ζ14+ζ22ζ14−ζ22ζ14−ζ22ζ14+ζ62+ζ70ζ14+ζ62+ζ70−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ700-113−3000000
χ1922-2-2-1001-11−3−3332-2ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70ζ14+ζ62+ζ70ζ14+ζ62+ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ14−ζ22ζ14−ζ22−ζ14+ζ22−ζ14+ζ220-11−33000000
χ2022-2-2-1001-11−3−3332-2ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ14−ζ22ζ14−ζ22−ζ14+ζ22−ζ14+ζ22−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70ζ14+ζ62+ζ70ζ14+ζ62+ζ700-11−33000000
χ2122-2-2-1001-11−3−3332-2−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ14−ζ22ζ14−ζ22−ζ14+ζ22−ζ14+ζ22−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70ζ14+ζ62+ζ70ζ14+ζ62+ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ700-11−33000000
χ222-2-2222-22-2-22-22-200-1-1-1111111-1-1-11-11-11-11-11-11-100000−i2i2−i2i200
χ232-2-2222-22-2-22-22-200-1-1-1111111-1-1-11-11-11-11-11-11-100000i2−i2i2−i200
χ242-2-222-222-2-2-22-2200-1-1-1111111-1-1-1-11-11-11-11-11-1100000−i2i2i2−i200
χ252-2-222-222-2-2-22-2200-1-1-1111111-1-1-1-11-11-11-11-11-1100000i2−i2−i2i200
χ2633333333333333-1-1000000000000000000000000-1-1-1-1-11111-1-1
χ2733333333333333-1-1000000000000000000000000-1-1-1-1-1-1-1-1-111
χ2833333-3-3333-3-3-3-3-1-10000000000000000000000001-1-11111-1-1-11
χ2933333-3-3333-3-3-3-3-1-10000000000000000000000001-1-111-1-1111-1
χ304-44-4400-4-44000000111-11-11-11-1-1-13−3−333−3−333−3−3300000000000
χ314-44-4400-4-44000000111-11-11-11-1-1-1−333−3−333−3−333−300000000000
χ324-44-4400-4-44000000-2-2-22-22-22-222200000000000000000000000
χ334-44-4-20022-223−23−232300−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ14+ζ62+ζ70−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70ζ14+ζ62+ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ14+ζ22ζ14−ζ22ζ14−ζ22−ζ14+ζ2200000000000
χ344-44-4-20022-223−23−232300ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ14+ζ22ζ14−ζ22ζ14−ζ22−ζ14+ζ22ζ14+ζ62+ζ70−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70ζ14+ζ62+ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ7000000000000
χ354-44-4-20022-223−23−232300−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ14+ζ22ζ14−ζ22ζ14−ζ22−ζ14+ζ22ζ14+ζ62+ζ70−ζ14−ζ62−ζ70−ζ14−ζ62−ζ70ζ14+ζ62+ζ7000000000000
χ364-44-4-20022-2−232323−2300−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ14−ζ62−ζ70ζ14+ζ62+ζ70ζ14+ζ62+ζ70−ζ14−ζ62−ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ14−ζ22−ζ14+ζ22−ζ14+ζ22ζ14−ζ2200000000000
χ374-44-4-20022-2−232323−2300ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ14−ζ22−ζ14+ζ22−ζ14+ζ22ζ14−ζ22−ζ14−ζ62−ζ70ζ14+ζ62+ζ70ζ14+ζ62+ζ70−ζ14−ζ62−ζ70ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ7000000000000
χ384-44-4-20022-2−232323−2300−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ22+ζ62+ζ70−ζ22−ζ62−ζ70−ζ22−ζ62−ζ70ζ22+ζ62+ζ70ζ14−ζ22−ζ14+ζ22−ζ14+ζ22ζ14−ζ22−ζ14−ζ62−ζ70ζ14+ζ62+ζ70ζ14+ζ62+ζ70−ζ14−ζ62−ζ7000000000000
χ394-4-4444-44-4-44-44-400111-1-1-1-1-1-1111-11-11-11-11-11-1100000000000
χ404-4-444-444-4-4-44-4400111-1-1-1-1-1-11111-11-11-11-11-11-100000000000
χ414-4-44-24-4-222-22-2200−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68−ζ4−ζ68ζ4+ζ6800000000000
χ424-4-44-24-4-222-22-2200ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4−ζ44+ζ52−ζ4+ζ44−ζ5200000000000
χ434-4-44-24-4-222-22-2200−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4−ζ44+ζ52−ζ4+ζ44−ζ52−ζ4−ζ68ζ4+ζ68−ζ4−ζ68ζ4+ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ6800000000000
χ444-4-44-2-44-2222-22-200−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4−ζ44+ζ52ζ4+ζ68−ζ4−ζ68ζ4+ζ68−ζ4−ζ6800000000000
χ454-4-44-2-44-2222-22-200ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ4−ζ68ζ4+ζ68−ζ4−ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4−ζ44+ζ5200000000000
χ464-4-44-2-44-2222-22-200−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4−ζ44+ζ52−ζ4+ζ44−ζ52ζ4−ζ44+ζ52ζ4+ζ68−ζ4−ζ68ζ4+ζ68−ζ4−ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ68−ζ44+ζ52−ζ68ζ44−ζ52+ζ6800000000000
χ476666-366-3-3-3-3-3-3-3-2-2000000000000000000000000-21111000000
χ486666-3-6-6-3-3-33333-2-2000000000000000000000000211-1-1000000
χ4966-6-6600-66-60000-220000000000000000000000000-2200000000
χ5066-6-6-3003-333333−33−33-2200000000000000000000000001-1−33000000
χ5166-6-6-3003-33−33−333333-2200000000000000000000000001-13−3000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.