Finite Group Databasebeta

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C23×C11×C121 #72189206

order10648
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 22360800
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C11

Aliases

abelianC23×C11×C121

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC11C23×C112
socle, prime radicalC23×C112C11
LCSG ▷ C1
UCSC1 ◁ G

416 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C11×C121, C24×C11×C121, C23×C3×C11×C121
maximal normal subgroup ofC22×C4×C11×C121, C24×C11×C121, C23×C3×C11×C121
maximal quotient ofC22×C4×C11×C121, C24×C11×C121, C23×C3×C11×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.