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C3×C11×C3⋊#261 #19104208

order5148
isoclinismisoclinic class of C3⋊#261
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C3⋊#261
unambiguous semidirect productC3⋊(C3×C11×#261)

Splittings

Fitting, socle, HallC32×C11×C13 ⋊ C4
derivedC3×C13 ⋊ C3×C4×C11
HallC11×C13 ⋊ C3×Dic3
HallC32×C13 ⋊ C4×C11
HallC32×C11 ⋊ #261
SylowC13 ⋊ C3×C11×Dic3
SylowC32 ⋊ C11×#261

Subgroups

subgroupG/H
center, hypercenterC3×C11C3⋊#261
commutator, hypocenterC3×C13C3×C4×C11
FrattiniC1G
Fitting, socleC32×C11×C13C4
LCSG ▷ C3×C13
UCSC1 ◁ C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

495 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×C3⋊#261, C3×C5×C11×C3⋊#261, C3×C11×C3⋊#63122, …
maximal normal subgroup ofC3×C11⋊C5×C3⋊#261, C3×C5×C11×C3⋊#261, C3×C7×C11×C3⋊#261
maximal quotient ofC3×C5×C11×C3⋊#261, C3×C11×C3⋊#63122, C3×C11×C3⋊#63121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 84);