Finite Group Databasebeta

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C33×C11×C32 #72188236

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1797120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33

Aliases

abelianC33×C11×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C2×C33×C11
socle, prime radicalC2×C33×C11C16
LCSG ▷ C1
UCSC1 ◁ G

336 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 ofC33×C11×C64, C2×C33×C11×C32, C32×C9×C11×C32, …
maximal normal subgroup ofC33×C11×C64, C2×C33×C11×C32, C32×C9×C11×C32, …
maximal quotient ofC33×C11×C64, C2×C33×C11×C32, C32×C9×C11×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.