Finite Group Databasebeta

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C22×C3×C42×C5×C23 #72199576

order22080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 25952256
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C3×C42×C5×C23
multiplicative(ℤ/33605)ˣ, (ℤ/43005)ˣ, (ℤ/45705)ˣ, (ℤ/45825)ˣ, (ℤ/45872)ˣ, (ℤ/47944)ˣ, (ℤ/48405)ˣ, (ℤ/48752)ˣ, (ℤ/51632)ˣ, (ℤ/55240)ˣ, (ℤ/55280)ˣ, (ℤ/55400)ˣ, (ℤ/55600)ˣ, (ℤ/57340)ˣ, (ℤ/60940)ˣ, (ℤ/61100)ˣ, (ℤ/64540)ˣ, (ℤ/66288)ˣ, (ℤ/66384)ˣ, (ℤ/67210)ˣ, (ℤ/71916)ˣ, (ℤ/82860)ˣ, (ℤ/82980)ˣ, (ℤ/83100)ˣ, (ℤ/86010)ˣ, (ℤ/91410)ˣ, (ℤ/91650)ˣ, (ℤ/96810)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C3×C5×C23
socle, prime radicalC24×C3×C5×C23C22
LCSG ▷ C1
UCSC1 ◁ G

1992 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

22080 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.