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C11×C3⋊(C7⋊#261) #26046551

order12012
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C7⋊#261)
unambiguous semidirect productC3⋊(C11×C7⋊#261)
unambiguous semidirect productC7⋊(C11×C3⋊#261)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C4
derived, HallC3×C7×C13 ⋊ C4×C11
HallC7×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ Dic7
HallC3×C7×C11 ⋊ #261
HallC11×C13 ⋊ Dic21
HallC7×C13 ⋊ C11×Dic3
HallC7×C11 ⋊ C3⋊#261
HallC3×C13 ⋊ C11×Dic7
HallC3×C11 ⋊ C7⋊#261
HallC3×C7 ⋊ C11×#261
SylowC13 ⋊ C11×Dic21
SylowC7 ⋊ C11×C3⋊#261
SylowC3 ⋊ C11×C7⋊#261

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C4
prime radicalC3×C7×C11×D13C2
cosocleC3×C7×D13C2×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

957 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×C7⋊(C9⋊#261), C11×C3⋊#11763984, C11×C3⋊#11763985, …
maximal normal subgroup ofC11×C3⋊#11763984, C11×C3⋊#11763985, C11×C3⋊(ΓL(1,𝔽8)⋊#261), …
maximal quotient ofC11×C7⋊(C9⋊#261), C3×C11×C3⋊(C7⋊#261), C11×C3⋊(C3⋊(C7⋊#261))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 141);