Finite Group Databasebeta

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C23×C42×C8×C11 #72189781

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 43293270343680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C212×C43

Aliases

abelianC23×C42×C8×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C26×C11
socle, prime radicalC26×C11C22×C4
LCSG ▷ C1
UCSC1 ◁ G

111402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C42×C11×C16, C23×C4×C82×C11, C22×C43×C8×C11, …
maximal normal subgroup ofC23×C42×C11×C16, C23×C4×C82×C11, C22×C43×C8×C11, …
maximal quotient ofC23×C42×C11×C16, C23×C4×C82×C11, C22×C43×C8×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.