Finite Group Databasebeta

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C22×C3×C42×C9×C13 #72199879

order22464
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 191102976
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C42×C9×C13
multiplicative(ℤ/35245)ˣ, (ℤ/39273)ˣ, (ℤ/41181)ˣ, (ℤ/43845)ˣ, (ℤ/44745)ˣ, (ℤ/45315)ˣ, (ℤ/46472)ˣ, (ℤ/46768)ˣ, (ℤ/47728)ˣ, (ℤ/48165)ˣ, (ℤ/50024)ˣ, (ℤ/50085)ˣ, (ℤ/51376)ˣ, (ℤ/52364)ˣ, (ℤ/54908)ˣ, (ℤ/58460)ˣ, (ℤ/59660)ˣ, (ℤ/64220)ˣ, (ℤ/67824)ˣ, (ℤ/69708)ˣ, (ℤ/70490)ˣ, (ℤ/70596)ˣ, (ℤ/73008)ˣ, (ℤ/74412)ˣ, (ℤ/75036)ˣ, (ℤ/78546)ˣ, (ℤ/82362)ˣ, (ℤ/84780)ˣ, (ℤ/87690)ˣ, (ℤ/89490)ˣ, (ℤ/90630)ˣ, (ℤ/91260)ˣ, (ℤ/96330)ˣ, (ℤ/100170)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C24×C32×C13
socle, prime radicalC24×C32×C13C22×C3
LCSG ▷ C1
UCSC1 ◁ G

4980 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

22464 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.