Finite Group Databasebeta

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C3×C4×C52×C32 #72188303

order9600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 491520
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4×C5

Aliases

abelianC3×C4×C52×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C22×C3×C52
socle, prime radicalC22×C3×C52C2×C16
LCSG ▷ C1
UCSC1 ◁ G

576 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 ofC3×C4×C52×C64, C3×C52×C8×C32, C2×C3×C4×C52×C32, …
maximal normal subgroup ofC3×C4×C52×C64, C3×C52×C8×C32, C2×C3×C4×C52×C32, …
maximal quotient ofC3×C4×C52×C64, C3×C52×C8×C32, C2×C3×C4×C52×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.