Finite Group Databasebeta

← Group #13103517

Character table — Group #13103517

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222444444445555888888888888888888101010101010101010102020202020202020202020202020202020202020202020202020404040405050505050505050100100
order12224455101010101010510101020202020444455101010101010202020202020202020204420202020202020204488882020202040404040404040404040404040404040202020208888888844
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111ii−i−iii−i−i-1-1
χ61111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111−i−iii−i−iii-1-1
χ71111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1−i−iii−i−iii11
χ81111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1ii−i−iii−i−i11
χ91111-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ101111-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-1
χ111111-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ121111-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-11
χ131111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1i−i−ii1111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii-11
χ141111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1−iii−i1111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i-11
χ151111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11i−i−ii1111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i1-1
χ161111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11−iii−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii1-1
χ17222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+52002i2i−2i−2i1−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ1400000000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+5200−2i−2i2i2i1−521−521+521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ1400000000000000
χ21222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000
χ22222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−52002i2i−2i−2i1+521+521−521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ3800000000000000
χ24222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−5200−2i−2i2i2i1+521+521−521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ3800000000000000
χ252222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222221−521−521+521+522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000
χ262222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222221−521−521+521+522222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-22-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000
χ272222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222221−521−521+521+52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+52002i−2i−2i2i−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ1400000000000000
χ282222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222221−521−521+521+52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+5200−2i2i2i−2i−1+52−1+52−1−52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ1400000000000000
χ292222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222221+521+521−521−522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002-22-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000
χ302222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222221+521+521−521−522222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-22-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000
χ312222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222221+521+521−521−52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52221+521+521−521−521+521+521−521−52002i−2i−2i2i−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ3800000000000000
χ322222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222221+521+521−521−52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-21+521+521+521+521−521−521−521−52221+521+521−521−521+521+521−521−5200−2i2i2i−2i−1−52−1−52−1+52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ3800000000000000
χ3322-2-20022-2-22-22-222-2-2000022-2-2222-22-2-2-20000000000002222-2-2-2-20000000000000000000000000000002-22-2000000
χ3422-2-20022-2-22-22-222-2-2000022-2-2222-22-2-2-20000000000002222-2-2-2-2000000000000000000000000000000-22-22000000
χ3522-2-20022-2-22-22-222-2-20000-2-222222-22-2-2-2000000000000-2-2-2-222220000000000000000000000000000002i−2i−2i2i000000
χ3622-2-20022-2-22-22-222-2-20000-2-222222-22-2-2-2000000000000-2-2-2-22222000000000000000000000000000000−2i2i2i−2i000000
χ372-22-22-22222-2-2-2-22-2-222-22-22i−2i2i−2i22-2-2-2-2222-222-2-222-2-22i−2i2i−2i2i−2i2i−2i2i−2i0000002i−2i2i−2i000000000000000000000000000000
χ382-22-22-22222-2-2-2-22-2-222-22-2−2i2i−2i2i22-2-2-2-2222-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i000000−2i2i−2i2i000000000000000000000000000000
χ392-22-22-2−1+52−1−52−1+52−1−521−521−521+521+522-2-22−1+521−52−1−521+522i−2i2i−2i−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1+521−521−52−1−52−1−521+521+522i−2i−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14000000−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ13+ζ37ζ13−ζ37−ζ21+ζ29ζ21−ζ29−ζ13+ζ37ζ13−ζ37−ζ21+ζ29ζ21−ζ29ζ7−ζ23−ζ7+ζ23−ζ31+ζ39ζ31−ζ39ζ7−ζ23−ζ7+ζ23−ζ31+ζ39ζ31−ζ3900000000000000
χ402-22-22-2−1+52−1−52−1+52−1−521−521−521+521+522-2-22−1+521−52−1−521+522i−2i2i−2i−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1+521−521−52−1−52−1−521+521+522i−2i−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14000000−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14ζ13−ζ37−ζ13+ζ37ζ21−ζ29−ζ21+ζ29ζ13−ζ37−ζ13+ζ37ζ21−ζ29−ζ21+ζ29−ζ7+ζ23ζ7−ζ23ζ31−ζ39−ζ31+ζ39−ζ7+ζ23ζ7−ζ23ζ31−ζ39−ζ31+ζ3900000000000000
χ412-22-22-2−1+52−1−52−1+52−1−521−521−521+521+522-2-22−1+521−52−1−521+52−2i2i−2i2i−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1+521−521−52−1−52−1−521+521+52−2i2iζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14000000ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ7−ζ23−ζ7+ζ23−ζ31+ζ39ζ31−ζ39ζ7−ζ23−ζ7+ζ23−ζ31+ζ39ζ31−ζ39−ζ13+ζ37ζ13−ζ37−ζ21+ζ29ζ21−ζ29−ζ13+ζ37ζ13−ζ37−ζ21+ζ29ζ21−ζ2900000000000000
χ422-22-22-2−1+52−1−52−1+52−1−521−521−521+521+522-2-22−1+521−52−1−521+52−2i2i−2i2i−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1+521−521−52−1−52−1−521+521+52−2i2iζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14000000ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14−ζ7+ζ23ζ7−ζ23ζ31−ζ39−ζ31+ζ39−ζ7+ζ23ζ7−ζ23ζ31−ζ39−ζ31+ζ39ζ13−ζ37−ζ13+ζ37ζ21−ζ29−ζ21+ζ29ζ13−ζ37−ζ13+ζ37ζ21−ζ29−ζ21+ζ2900000000000000
χ432-22-22-2−1−52−1+52−1−52−1+521+521+521−521−522-2-22−1−521+52−1+521−522i−2i2i−2i−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1−521+521+52−1+52−1+521−521−522i−2i−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38000000−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ21+ζ29ζ21−ζ29ζ13−ζ37−ζ13+ζ37−ζ21+ζ29ζ21−ζ29ζ13−ζ37−ζ13+ζ37−ζ31+ζ39ζ31−ζ39−ζ7+ζ23ζ7−ζ23−ζ31+ζ39ζ31−ζ39−ζ7+ζ23ζ7−ζ2300000000000000
χ442-22-22-2−1−52−1+52−1−52−1+521+521+521−521−522-2-22−1−521+52−1+521−522i−2i2i−2i−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1−521+521+52−1+52−1+521−521−522i−2i−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38000000−ζ6−ζ14ζ6+ζ14−ζ22−ζ38ζ22+ζ38ζ21−ζ29−ζ21+ζ29−ζ13+ζ37ζ13−ζ37ζ21−ζ29−ζ21+ζ29−ζ13+ζ37ζ13−ζ37ζ31−ζ39−ζ31+ζ39ζ7−ζ23−ζ7+ζ23ζ31−ζ39−ζ31+ζ39ζ7−ζ23−ζ7+ζ2300000000000000
χ452-22-22-2−1−52−1+52−1−52−1+521+521+521−521−522-2-22−1−521+52−1+521−52−2i2i−2i2i−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1−521+521+52−1+52−1+521−521−52−2i2iζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38000000ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38−ζ31+ζ39ζ31−ζ39−ζ7+ζ23ζ7−ζ23−ζ31+ζ39ζ31−ζ39−ζ7+ζ23ζ7−ζ23−ζ21+ζ29ζ21−ζ29ζ13−ζ37−ζ13+ζ37−ζ21+ζ29ζ21−ζ29ζ13−ζ37−ζ13+ζ3700000000000000
χ462-22-22-2−1−52−1+52−1−52−1+521+521+521−521−522-2-22−1−521+52−1+521−52−2i2i−2i2i−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1−521+521+52−1+52−1+521−521−52−2i2iζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38000000ζ6+ζ14−ζ6−ζ14ζ22+ζ38−ζ22−ζ38ζ31−ζ39−ζ31+ζ39ζ7−ζ23−ζ7+ζ23ζ31−ζ39−ζ31+ζ39ζ7−ζ23−ζ7+ζ23ζ21−ζ29−ζ21+ζ29−ζ13+ζ37ζ13−ζ37ζ21−ζ29−ζ21+ζ29−ζ13+ζ37ζ13−ζ3700000000000000
χ472-22-2-222222-2-2-2-22-2-22-22-222i−2i2i−2i22-2-2-2-222-22-2-222-2-222−2i2i2i−2i2i−2i2i−2i2i−2i000000−2i2i−2i2i000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.