Finite Group Databasebeta

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C3×C4×C11×C81 #72189237

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 19440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C4×C11×C81

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C27C2×C32×C11
socle, prime radicalC2×C32×C11C2×C27
LCSG ▷ C1
UCSC1 ◁ G

108 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 ofC3×C8×C11×C81, C2×C3×C4×C11×C81, C3×C4×C11×C243, …
maximal normal subgroup ofC3×C8×C11×C81, C2×C3×C4×C11×C81, C3×C4×C11×C243, …
maximal quotient ofC3×C8×C11×C81, C2×C3×C4×C11×C81, C3×C4×C11×C243, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.