Finite Group Databasebeta

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C3×C5×C7×C9×C11 #72189054

order10395
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 25920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C5×C7×C9×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C32×C5×C7×C11
socle, prime radicalC32×C5×C7×C11C3
LCSG ▷ C1
UCSC1 ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10395 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C7×C9×C11, C3×C5×C7×C11×C27, C5×C7×C92×C11, …
maximal normal subgroup ofC2×C3×C5×C7×C9×C11, C3×C5×C7×C11×C27, C5×C7×C92×C11, …
maximal quotient ofC2×C3×C5×C7×C9×C11, C3×C5×C7×C11×C27, C5×C7×C92×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.