Finite Group Databasebeta

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C23×C3×C42×C25 #72188322

order9600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2642411520
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C42×C25
multiplicative(ℤ/28280)ˣ, (ℤ/31512)ˣ, (ℤ/33936)ˣ, (ℤ/36240)ˣ, (ℤ/36360)ˣ, (ℤ/39000)ˣ, (ℤ/42000)ˣ, (ℤ/42420)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C5C25×C3×C5
socle, prime radicalC25×C3×C5C22×C5
LCSG ▷ C1
UCSC1 ◁ G

9000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C8×C25, C22×C3×C43×C25, C24×C3×C42×C25, …
maximal normal subgroup ofC23×C3×C4×C8×C25, C22×C3×C43×C25, C24×C3×C42×C25, …
maximal quotient ofC23×C3×C4×C8×C25, C22×C3×C43×C25, C24×C3×C42×C25, …
automorphism group ofC5×C7×C8×C101, C3×C8×C13×C101
outer automorphism group ofC5×C7×C8×C101, C3×C8×C13×C101

GAP

Past the SmallGroups library coverage — no SmallGroups id.