Finite Group Databasebeta

← Group #10604914

Character table — Group #10604914

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111144444888888810101010202020202020202040111144444888888810101010202020202020202040
order12224510101021010101020204444888888884222241010101021010101020204444888888884
χ11111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11
χ31111111111111111-1-1-1-1iiii−i−i−i−i-11111111111111111-1-1-1-1iiii−i−i−i−i-1
χ41111111111111111-1-1-1-1−i−i−i−iiiii-11111111111111111-1-1-1-1−i−i−i−iiiii-1
χ5111111111-1-1-1-1-111111111-1-111-1-1-1111111111-1-1-1-1-111111111-1-111-1-1-1
χ6111111111-1-1-1-1-1111111-1-111-1-111-1111111111-1-1-1-1-1111111-1-111-1-111-1
χ7111111111-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1111111111-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1
χ8111111111-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1111111111-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1
χ92222-2222200000-2-222-2-20000000002222-2222200000-2-222-2-2000000000
χ102222-2222200000-2-2-2-2220000000002222-2222200000-2-2-2-222000000000
χ1122-2-2022-2-20000000002i−2i1+i−1−i001−i−1+i00022-2-2022-2-20000000002i−2i1+i−1−i001−i−1+i000
χ1222-2-2022-2-20000000002i−2i−1−i1+i00−1+i1−i00022-2-2022-2-20000000002i−2i−1−i1+i00−1+i1−i000
χ1322-2-2022-2-2000000000−2i2i1−i−1+i001+i−1−i00022-2-2022-2-2000000000−2i2i1−i−1+i001+i−1−i000
χ1422-2-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i00022-2-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i000
χ152-22-202-22-200000002i−2i00001+i−1−i001−i−1+i02-22-202-22-200000002i−2i00001+i−1−i001−i−1+i0
χ162-22-202-22-200000002i−2i0000−1−i1+i00−1+i1−i02-22-202-22-200000002i−2i0000−1−i1+i00−1+i1−i0
χ172-22-202-22-20000000−2i2i00001−i−1+i001+i−1−i02-22-202-22-20000000−2i2i00001−i−1+i001+i−1−i0
χ182-22-202-22-20000000−2i2i0000−1+i1−i00−1−i1+i02-22-202-22-20000000−2i2i0000−1+i1−i00−1−i1+i0
χ1944444-1-1-1-14-1-1-1-1-1-1000000000000044444-1-1-1-14-1-1-1-1-1-10000000000000
χ2044444-1-1-1-1-41111-1-1000000000000044444-1-1-1-1-41111-1-10000000000000
χ214444-4-1-1-1-1055−5−51100000000000004444-4-1-1-1-1055−5−5110000000000000
χ224444-4-1-1-1-10−5−5551100000000000004444-4-1-1-1-10−5−555110000000000000
χ234-4-4404-4-44000000000000000000004-4-4404-4-4400000000000000000000
χ244-4-440-111-10−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ185−500000000000004-4-440-111-10−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ185−50000000000000
χ254-4-440-111-10−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−5500000000000004-4-440-111-10−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−550000000000000
χ264-4-440-111-10ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ185−500000000000004-4-440-111-10ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ185−50000000000000
χ274-4-440-111-10ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−5500000000000004-4-440-111-10ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−550000000000000
χ2888-8-80-2-2220000000000000000000088-8-80-2-22200000000000000000000
χ298-88-80-22-22000000000000000000008-88-80-22-2200000000000000000000
χ3011111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1
χ321111111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1
χ331111111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1
χ34111111111-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111
χ35111111111-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-111-1-11
χ36111111111-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1-1-1-1-1-1-1-1-1-111111-1-11111−i−iiiii−i−i-1
χ37111111111-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1-1-1-1-1-1-1-1-1-111111-1-11111ii−i−i−i−iii-1
χ382222-2222200000-2-222-2-2000000000-2-2-2-22-2-2-2-20000022-2-222000000000
χ392222-2222200000-2-2-2-222000000000-2-2-2-22-2-2-2-2000002222-2-2000000000
χ4022-2-2022-2-20000000002i−2i1+i−1−i001−i−1+i000-2-2220-2-222000000000−2i2i−1−i1+i00−1+i1−i000
χ4122-2-2022-2-20000000002i−2i−1−i1+i00−1+i1−i000-2-2220-2-222000000000−2i2i1+i−1−i001−i−1+i000
χ4222-2-2022-2-2000000000−2i2i1−i−1+i001+i−1−i000-2-2220-2-2220000000002i−2i−1+i1−i00−1−i1+i000
χ4322-2-2022-2-2000000000−2i2i−1+i1−i00−1−i1+i000-2-2220-2-2220000000002i−2i1−i−1+i001+i−1−i000
χ442-22-202-22-200000002i−2i00001+i−1−i001−i−1+i0-22-220-22-220000000−2i2i0000−1−i1+i00−1+i1−i0
χ452-22-202-22-200000002i−2i0000−1−i1+i00−1+i1−i0-22-220-22-220000000−2i2i00001+i−1−i001−i−1+i0
χ462-22-202-22-20000000−2i2i00001−i−1+i001+i−1−i0-22-220-22-2200000002i−2i0000−1+i1−i00−1−i1+i0
χ472-22-202-22-20000000−2i2i0000−1+i1−i00−1−i1+i0-22-220-22-2200000002i−2i00001−i−1+i001+i−1−i0
χ4844444-1-1-1-14-1-1-1-1-1-10000000000000-4-4-4-4-41111-41111110000000000000
χ4944444-1-1-1-1-41111-1-10000000000000-4-4-4-4-411114-1-1-1-1110000000000000
χ504444-4-1-1-1-1055−5−5110000000000000-4-4-4-4411110−5−555-1-10000000000000
χ514444-4-1-1-1-10−5−555110000000000000-4-4-4-441111055−5−5-1-10000000000000
χ524-4-4404-4-4400000000000000000000-444-40-444-400000000000000000000
χ534-4-440-111-10−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ185−50000000000000-444-401-1-110ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−550000000000000
χ544-4-440-111-10−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−550000000000000-444-401-1-110ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ185−50000000000000
χ554-4-440-111-10ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ185−50000000000000-444-401-1-110−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−550000000000000
χ564-4-440-111-10ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−550000000000000-444-401-1-110−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ185−50000000000000
χ5788-8-80-2-22200000000000000000000-8-888022-2-200000000000000000000
χ588-88-80-22-2200000000000000000000-88-8802-22-200000000000000000000

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