Finite Group Databasebeta

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C24×C32×C4×C5×C9 #72203109

order25920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 963158999040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C33

Aliases

abelianC24×C32×C4×C5×C9
multiplicative(ℤ/57057)ˣ, (ℤ/61256)ˣ, (ℤ/61845)ˣ, (ℤ/64232)ˣ, (ℤ/64904)ˣ, (ℤ/65835)ˣ, (ℤ/65968)ˣ, (ℤ/76076)ˣ, (ℤ/82460)ˣ, (ℤ/82584)ˣ, (ℤ/83448)ˣ, (ℤ/84816)ˣ, (ℤ/87048)ˣ, (ℤ/91224)ˣ, (ℤ/91884)ˣ, (ℤ/92232)ˣ, (ℤ/93744)ˣ, (ℤ/96348)ˣ, (ℤ/97356)ˣ, (ℤ/97812)ˣ, (ℤ/102564)ˣ, (ℤ/106020)ˣ, (ℤ/108108)ˣ, (ℤ/114114)ˣ, (ℤ/117180)ˣ, (ℤ/119700)ˣ, (ℤ/123690)ˣ, (ℤ/131670)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C25×C33×C5
socle, prime radicalC25×C33×C5C2×C3
LCSG ▷ C1
UCSC1 ◁ G

68100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

25920 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.