Finite Group Databasebeta

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C22×C3×C42×C9×C11 #72196757

order19008
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 159252480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C42×C9×C11
multiplicative(ℤ/28405)ˣ, (ℤ/29785)ˣ, (ℤ/33189)ˣ, (ℤ/37185)ˣ, (ℤ/38295)ˣ, (ℤ/38805)ˣ, (ℤ/39664)ˣ, (ℤ/40365)ˣ, (ℤ/41288)ˣ, (ℤ/41392)ˣ, (ℤ/41685)ˣ, (ℤ/44252)ˣ, (ℤ/44464)ˣ, (ℤ/49580)ˣ, (ℤ/51740)ˣ, (ℤ/55580)ˣ, (ℤ/56810)ˣ, (ℤ/57168)ˣ, (ℤ/59570)ˣ, (ℤ/61932)ˣ, (ℤ/66378)ˣ, (ℤ/71460)ˣ, (ℤ/74370)ˣ, (ℤ/76590)ˣ, (ℤ/77610)ˣ, (ℤ/80730)ˣ, (ℤ/83370)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C24×C32×C11
socle, prime radicalC24×C32×C11C22×C3
LCSG ▷ C1
UCSC1 ◁ G

4980 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

19008 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.