Finite Group Databasebeta

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C23×C3×C42×C32 #72190665

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 34634616274944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C212×C43

Aliases

abelianC23×C3×C42×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C16C26×C3
socle, prime radicalC26×C3C22×C16
LCSG ▷ C1
UCSC1 ◁ G

198774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C42×C64, C23×C3×C4×C8×C32, C22×C3×C43×C32, …
maximal normal subgroup ofC23×C3×C42×C64, C23×C3×C4×C8×C32, C22×C3×C43×C32, …
maximal quotient ofC23×C3×C42×C64, C23×C3×C4×C8×C32, C22×C3×C43×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.