Finite Group Databasebeta

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C22×C3×C92×C11 #72189247

order10692
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 37791360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C32×C9

Aliases

abelianC22×C3×C92×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C22×C33×C11
socle, prime radicalC22×C33×C11C32
LCSG ▷ C1
UCSC1 ◁ G

1260 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×C3×C4×C92×C11, C23×C3×C92×C11, C22×C3×C9×C11×C27, …
maximal normal subgroup ofC2×C3×C4×C92×C11, C23×C3×C92×C11, C22×C3×C9×C11×C27, …
maximal quotient ofC2×C3×C4×C92×C11, C23×C3×C92×C11, C22×C3×C9×C11×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.