Finite Group Databasebeta

← Group #65534

Character table — Group #65534

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1122222224444444444444444444444444444444444442020404040
order1224455101022444410101010101010101010202020202020202020202020202020202020202044288
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1
χ31111111111-11-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1
χ41111111111-11-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11
χ5111111111-11-11-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11
χ6111111111-11-11-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1
χ7111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1
χ8111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-111
χ922222−1+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+52−1+52−1+52−1−52−1−52−1−52−1−5200000
χ1022222−1+52−1−52−1+52−1−522-22-2-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5200000
χ1122222−1+52−1−52−1+52−1−52-22-22-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+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+5200000
χ1222222−1+52−1−52−1+52−1−52-2-2-2-222−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000
χ1322222−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000
χ1422222−1−52−1+52−1−52−1+522-22-2-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200000
χ1522222−1−52−1+52−1−52−1+52-22-22-2-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200000
χ1622222−1−52−1+52−1−52−1+52-2-2-2-222−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000
χ17222-2-2222200002-22200000000-2-2-2-20000000022-2-222-2-200000
χ18222-2-222220000-222200000000-2-2-2-200000000-2-222-2-22200000
χ19222-2-2−1+52−1−52−1+52−1−5200002-2−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+521−521−52−1−52−1−521+521+5200000
χ20222-2-2−1+52−1−52−1+52−1−5200002-2−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+521−521−52−1−52−1−521+521+5200000
χ21222-2-2−1+52−1−52−1+52−1−520000-22−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−52−1+52−1+521+521+52−1−52−1−5200000
χ22222-2-2−1+52−1−52−1+52−1−520000-22−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−52−1+52−1+521+521+52−1−52−1−5200000
χ23222-2-2−1−52−1+52−1−52−1+5200002-2−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−521+521+52−1+52−1+521−521−5200000
χ24222-2-2−1−52−1+52−1−52−1+5200002-2−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−521+521+52−1+52−1+521−521−5200000
χ25222-2-2−1−52−1+52−1−52−1+520000-22−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+52−1−52−1−521−521−52−1+52−1+5200000
χ26222-2-2−1−52−1+52−1−52−1+520000-22−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+52−1−52−1−521−521−52−1+52−1+5200000
χ2722-22-22222020-200-2-2000022222-22-20000-2-2-2-20000000000000
χ2822-22-222220-20200-2-20000-2-2-2-22-22-2000022220000000000000
χ2922-22-2−1+52−1−52−1+52−1−52020-2001−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ1800000
χ3022-22-2−1+52−1−52−1+52−1−52020-2001−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ1800000
χ3122-22-2−1+52−1−52−1+52−1−520-202001−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ1800000
χ3222-22-2−1+52−1−52−1+52−1−520-202001−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ1800000
χ3322-22-2−1−52−1+52−1−52−1+52020-2001+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ1400000
χ3422-22-2−1−52−1+52−1−52−1+52020-2001+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ1400000
χ3522-22-2−1−52−1+52−1−52−1+520-202001+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ1400000
χ3622-22-2−1−52−1+52−1−52−1+520-202001+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ1400000
χ3722-2-22222220-2000-2-222220000-22-22-2-2-2-200000000000000000
χ3822-2-222222-202000-2-2-2-2-2-20000-22-22222200000000000000000
χ3922-2-22−1+52−1−52−1+52−1−5220-20001−521+52−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−52−1+521+52−1−521−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000
χ4022-2-22−1+52−1−52−1+52−1−5220-20001−521+52−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−52−1+521+52−1−521−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000
χ4122-2-22−1+52−1−52−1+52−1−52-2020001−521+521−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−52−1+521+52−1−52−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000
χ4222-2-22−1+52−1−52−1+52−1−52-2020001−521+521−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−52−1+521+52−1−52−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000
χ4322-2-22−1−52−1+52−1−52−1+5220-20001+521−52−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+52−1−521−52−1+521+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000
χ4422-2-22−1−52−1+52−1−52−1+5220-20001+521−52−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+52−1−521−52−1+521+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000
χ4522-2-22−1−52−1+52−1−52−1+52-2020001+521−521+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+52−1−521−52−1+52−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000
χ4622-2-22−1−52−1+52−1−52−1+52-2020001+521−521+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+52−1−521−52−1+52−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000
χ474-400044-4-40000000000000000000000000000000000002i−2i000
χ484-400044-4-4000000000000000000000000000000000000−2i2i000
χ498-8000−2+25−2−252−252+2500000000000000000000000000000000000000000
χ508-8000−2−25−2+252+252−2500000000000000000000000000000000000000000

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