Finite Group Databasebeta

← Group #10602913

Character table — Group #10602913

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size112222222222222224444444444448888888888888888888888888888884040404040404040
order1222244445510102020202010101010101020202020202022448810101010101010102020202020202020404040404040404044444488
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111111111-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ9222222222−1+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+52−1−52222222−1+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+52−1−52−1−52−1−52−1−5200000000
χ10222222222−1+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+52−1−522-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5200000000
χ11222222222−1+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+52−1−52-22-22-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200000000
χ12222222222−1+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+52−1−52-2-2-2-2221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000
χ13222222222−1−52−1+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+52222222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000
χ14222222222−1−52−1+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+522-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200000000
χ15222222222−1−52−1+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+52-22-22-2-21+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+521−521−521−521−5200000000
χ16222222222−1−52−1+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+52-2-2-2-2221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000
χ1722222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000002-20000
χ1822222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000-220000
χ19222-2-222-2-2222222222-2-22-2-22-22-2-2-200000000000000000000000000000000002i−2i00
χ20222-2-222-2-2222222222-2-22-2-22-22-2-2-20000000000000000000000000000000000−2i2i00
χ21222-2-2-2-2222222-2-2-2-22-2-22-2-2-22-2222020-200000022220000-2-2-2-20000000000000000
χ22222-2-2-2-2222222-2-2-2-22-2-22-2-2-22-22220-202000000-2-2-2-2000022220000000000000000
χ23222-2-2-2-222−1+52−1−52−1+52−1−521−521−521+521+52−1+521−521−52−1−521+521+521−52−1+521+52−1−52−1+52−1−52020-200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800000000
χ24222-2-2-2-222−1+52−1−52−1+52−1−521−521−521+521+52−1+521−521−52−1−521+521+521−52−1+521+52−1−52−1+52−1−52020-200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800000000
χ25222-2-2-2-222−1+52−1−52−1+52−1−521−521−521+521+52−1+521−521−52−1−521+521+521−52−1+521+52−1−52−1+52−1−520-20200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800000000
χ26222-2-2-2-222−1+52−1−52−1+52−1−521−521−521+521+52−1+521−521−52−1−521+521+521−52−1+521+52−1−52−1+52−1−520-20200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800000000
χ27222-2-2-2-222−1−52−1+52−1−52−1+521+521+521−521−52−1−521+521+52−1+521−521−521+52−1−521−52−1+52−1−52−1+52020-200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ1400000000
χ28222-2-2-2-222−1−52−1+52−1−52−1+521+521+521−521−52−1−521+521+52−1+521−521−521+52−1−521−52−1+52−1−52−1+52020-200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1400000000
χ29222-2-2-2-222−1−52−1+52−1−52−1+521+521+521−521−52−1−521+521+52−1+521−521−521+52−1−521−52−1+52−1−52−1+520-20200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ1400000000
χ30222-2-2-2-222−1−52−1+52−1−52−1+521+521+521−521−52−1−521+521+52−1+521−521−521+52−1−521−52−1+52−1−52−1+520-20200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ1400000000
χ3122-22-22-22-222222222-22-2-22-2-2-2-2-22200002-200000000000000002-22-22-22-200000000
χ3222-22-22-22-222222222-22-2-22-2-2-2-2-2220000-220000000000000000-22-22-22-2200000000
χ3322-22-22-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−52−1+521−521+52−1−521+521−521−521+521+52−1+52−1−5200002-2ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+521−52−1+521−52−1−521+52−1−521+5200000000
χ3422-22-22-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−52−1+521−521+52−1−521+521−521−521+521+52−1+52−1−5200002-2−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+521−52−1+521−52−1−521+52−1−521+5200000000
χ3522-22-22-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−52−1+521−521+52−1−521+521−521−521+521+52−1+52−1−520000-22ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−52−1+521−52−1+521+52−1−521+52−1−5200000000
χ3622-22-22-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−52−1+521−521+52−1−521+521−521−521+521+52−1+52−1−520000-22−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−52−1+521−52−1+521+52−1−521+52−1−5200000000
χ3722-22-22-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+52−1−521+521−52−1+521−521+521+521−521−52−1−52−1+5200002-2−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−521+52−1−521+52−1+521−52−1+521−5200000000
χ3822-22-22-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+52−1−521+521−52−1+521−521+521+521−521−52−1−52−1+5200002-2ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−521+52−1−521+52−1+521−52−1+521−5200000000
χ3922-22-22-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+52−1−521+521−52−1+521−521+521+521−521−52−1−52−1+520000-22−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+52−1−521+52−1−521−52−1+521−52−1+5200000000
χ4022-22-22-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+52−1−521+521−52−1+521−521+521+521−521−52−1−52−1+520000-22ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+52−1−521+52−1−521−52−1+521−52−1+5200000000
χ4122-22-2-22-222222-2-2-2-2-22-2-22-22222-2-20000000000000000000000000000000000002-2
χ4222-22-2-22-222222-2-2-2-2-22-2-22-22222-2-2000000000000000000000000000000000000-22
χ4322-2-222-2-2222222222-2-22-2-22-22-22-2-20000000000000000000000000000002-2000000
χ4422-2-222-2-2222222222-2-22-2-22-22-22-2-2000000000000000000000000000000-22000000
χ4522-2-22-222-22222-2-2-2-2-2-22-2-222-22-22220-200022220000-2-2-2-200000000000000000000
χ4622-2-22-222-22222-2-2-2-2-2-22-2-222-22-222-202000-2-2-2-20000222200000000000000000000
χ4722-2-22-222-2−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+521−52−1−521+52−1+52−1−5220-2000−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000000
χ4822-2-22-222-2−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+521−52−1−521+52−1+52−1−5220-2000−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000000
χ4922-2-22-222-2−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+521−52−1−521+52−1+52−1−52-2020001−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000000
χ5022-2-22-222-2−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+521+521+52−1−52−1+521−52−1−521+52−1+52−1−52-2020001−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000000
χ5122-2-22-222-2−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−521+52−1+521−52−1−52−1+5220-2000−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000000
χ5222-2-22-222-2−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−521+52−1+521−52−1−52−1+5220-2000−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000000
χ5322-2-22-222-2−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−521+52−1+521−52−1−52−1+52-2020001+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000000
χ5422-2-22-222-2−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−521−521−52−1+52−1−521+52−1+521−52−1−52−1+52-2020001+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000000
χ5544444-4-4-4-4−1+5−1−5−1+5−1−51−51−51+51+5−1+5−1+5−1+5−1−5−1−5−1−51−51−51+51+51−51+500000000000000000000000000000000000000
χ5644444-4-4-4-4−1−5−1+5−1−5−1+51+51+51−51−5−1−5−1−5−1−5−1+5−1+5−1+51+51+51−51−51+51−500000000000000000000000000000000000000
χ57444-4-444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5−1+51−51−5−1−51+51+5−1+51−5−1−51+51−51+500000000000000000000000000000000000000
χ58444-4-444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5−1−51+51+5−1+51−51−5−1−51+5−1+51−51+51−500000000000000000000000000000000000000
χ5944-44-4-44-44−1+5−1−5−1+5−1−51−51−51+51+51−5−1+51−51+5−1−51+5−1+5−1+5−1−5−1−51−51+500000000000000000000000000000000000000
χ6044-44-4-44-44−1−5−1+5−1−5−1+51+51+51−51−51+5−1−51+51−5−1+51−5−1−5−1−5−1+5−1+51+51−500000000000000000000000000000000000000
χ6144-4-444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−51−51−5−1+51+51+5−1−51−5−1+51+5−1−51−51+500000000000000000000000000000000000000
χ6244-4-444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+51+51+5−1−51−51−5−1+51+5−1−51−5−1+51+51−500000000000000000000000000000000000000
χ638-8000000088-8-8000000000000000000000000000000000000000000000000000000
χ648-80000000−2+25−2−252−252+25−4ζ11+4ζ194ζ11−4ζ194ζ3−4ζ7−4ζ3+4ζ700000000000000000000000000000000000000000000000000
χ658-80000000−2+25−2−252−252+254ζ11−4ζ19−4ζ11+4ζ19−4ζ3+4ζ74ζ3−4ζ700000000000000000000000000000000000000000000000000
χ668-80000000−2−25−2+252+252−254ζ3−4ζ7−4ζ3+4ζ74ζ11−4ζ19−4ζ11+4ζ1900000000000000000000000000000000000000000000000000
χ678-80000000−2−25−2+252+252−25−4ζ3+4ζ74ζ3−4ζ7−4ζ11+4ζ194ζ11−4ζ1900000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.