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C3×C7×C11⋊#261 #26046533

order12012
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11⋊#261
unambiguous semidirect productC11⋊(C3×C7×#261)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C4
derived, HallC11×C13 ⋊ C3×C4×C7
HallC7×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ C4×C7
HallC3×C7×C13 ⋊ Dic11
HallC3×C7×C11 ⋊ #261
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#261
HallC3×C13 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×#261
SylowC13 ⋊ C3×C7×Dic11
SylowC11 ⋊ C3×C7×#261

Subgroups

subgroupG/H
center, hypercenterC3×C7C11⋊#261
commutator, hypocenterC11×C13C3×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C13C4
prime radicalC3×C7×C11×D13C2
cosocleC11×D13C2×C3×C7
LCSG ▷ C11×C13
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

987 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11⋊(#261⋊C9), C11⋊#15692589, C11⋊#15692588, …
maximal normal subgroup ofC7×C11⋊(#261⋊C9), C11⋊#15692589, C11⋊#15692588, …
maximal quotient ofC7×C9×C11⋊#261, C32×C7×C11⋊#261, C3×C7×C3⋊(C11⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 123);