Finite Group Databasebeta

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C22×C3×C42×C5×C27 #72203102

order25920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 191102976
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C42×C5×C27
multiplicative(ℤ/41965)ˣ, (ℤ/46761)ˣ, (ℤ/50685)ˣ, (ℤ/52845)ˣ, (ℤ/53192)ˣ, (ℤ/53955)ˣ, (ℤ/54064)ˣ, (ℤ/56264)ˣ, (ℤ/56368)ˣ, (ℤ/56805)ˣ, (ℤ/57225)ˣ, (ℤ/57915)ˣ, (ℤ/60592)ˣ, (ℤ/62348)ˣ, (ℤ/67580)ˣ, (ℤ/70460)ˣ, (ℤ/75740)ˣ, (ℤ/76300)ˣ, (ℤ/77904)ˣ, (ℤ/79056)ˣ, (ℤ/79788)ˣ, (ℤ/83930)ˣ, (ℤ/84396)ˣ, (ℤ/93522)ˣ, (ℤ/97380)ˣ, (ℤ/98100)ˣ, (ℤ/98820)ˣ, (ℤ/101370)ˣ, (ℤ/105300)ˣ, (ℤ/105690)ˣ, (ℤ/107910)ˣ, (ℤ/113610)ˣ, (ℤ/114450)ˣ, (ℤ/115830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C9C24×C32×C5
socle, prime radicalC24×C32×C5C22×C9
LCSG ▷ C1
UCSC1 ◁ G

6972 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.