Finite Group Databasebeta

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C32×C43×C16 #72187997

order9216
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 135291469824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C46

Aliases

abelianC32×C43×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C8C24×C32
socle, prime radicalC24×C32C23×C8
LCSG ▷ C1
UCSC1 ◁ G

28062 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C43×C32, C32×C42×C8×C16, C2×C32×C43×C16, …
maximal normal subgroup ofC32×C43×C32, C32×C42×C8×C16, C2×C32×C43×C16, …
maximal quotient ofC32×C43×C32, C32×C42×C8×C16, C2×C32×C43×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.