Finite Group Databasebeta

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C3×C9×C11×C32 #72188235

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 17280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C9×C11×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C16C2×C32×C11
socle, prime radicalC2×C32×C11C3×C16
LCSG ▷ C1
UCSC1 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C9×C11×C64, C2×C3×C9×C11×C32, C3×C11×C27×C32, …
maximal normal subgroup ofC3×C9×C11×C64, C2×C3×C9×C11×C32, C3×C11×C27×C32, …
maximal quotient ofC3×C9×C11×C64, C2×C3×C9×C11×C32, C3×C11×C27×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.