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C22×C32×C42×C5×C7 #72197787

order20160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 169869312
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C32×C42×C5×C7
multiplicative(ℤ/29029)ˣ, (ℤ/30745)ˣ, (ℤ/31465)ˣ, (ℤ/32305)ˣ, (ℤ/35035)ˣ, (ℤ/35061)ˣ, (ℤ/37149)ˣ, (ℤ/37323)ˣ, (ℤ/39345)ˣ, (ℤ/40455)ˣ, (ℤ/41145)ˣ, (ℤ/41535)ˣ, (ℤ/41925)ˣ, (ℤ/41968)ˣ, (ℤ/43784)ˣ, (ℤ/43888)ˣ, (ℤ/44205)ˣ, (ℤ/44835)ˣ, (ℤ/45675)ˣ, (ℤ/46748)ˣ, (ℤ/47152)ˣ, (ℤ/47775)ˣ, (ℤ/47824)ˣ, (ℤ/49532)ˣ, (ℤ/52460)ˣ, (ℤ/54860)ˣ, (ℤ/55900)ˣ, (ℤ/58058)ˣ, (ℤ/58940)ˣ, (ℤ/59780)ˣ, (ℤ/60624)ˣ, (ℤ/61490)ˣ, (ℤ/62930)ˣ, (ℤ/63684)ˣ, (ℤ/63700)ˣ, (ℤ/64610)ˣ, (ℤ/65676)ˣ, (ℤ/70070)ˣ, (ℤ/70122)ˣ, (ℤ/74298)ˣ, (ℤ/74646)ˣ, (ℤ/75780)ˣ, (ℤ/78690)ˣ, (ℤ/80910)ˣ, (ℤ/82290)ˣ, (ℤ/83070)ˣ, (ℤ/83850)ˣ, (ℤ/88410)ˣ, (ℤ/89670)ˣ, (ℤ/91350)ˣ, (ℤ/95550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C32×C5×C7
socle, prime radicalC24×C32×C5×C7C22
LCSG ▷ C1
UCSC1 ◁ G

5976 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

20160 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.