Finite Group Databasebeta

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C22×C32×C11×C27 #72189246

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4199040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C33

Aliases

abelianC22×C32×C11×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C33×C11
socle, prime radicalC22×C33×C11C9
LCSG ▷ C1
UCSC1 ◁ G

720 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10692 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C11×C27, C23×C32×C11×C27, C22×C32×C11×C81, …
maximal normal subgroup ofC2×C32×C4×C11×C27, C23×C32×C11×C27, C22×C32×C11×C81, …
maximal quotient ofC2×C32×C4×C11×C27, C23×C32×C11×C27, C22×C32×C11×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.