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C3×C7⋊(C11⋊#261) #26046537

order12012
automorphism?
homologyAbelianization (H1) = C3×C4 · 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, HallC7×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ Dic7
HallC3×C7×C13 ⋊ Dic11
HallC3×C7×C11 ⋊ #261
HallC11×C13 ⋊ C3×Dic7
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#261
HallC3×C13 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#261
HallC3×C7 ⋊ C11⋊#261
SylowC13 ⋊ C3×Dic77
SylowC11 ⋊ C3×C7⋊#261
SylowC7 ⋊ C3×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C11⋊#261)
commutator, hypocenterC7×C11×C13C3×C4
FrattiniC1G
Fitting, socleC3×C7×C11×C13C4
prime radicalC3×C7×C11×D13C2
cosocleC7×C11×D13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

933 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊#15692592, C11⋊#15692591, C11⋊((C7⋊C9)⋊#261), …
maximal normal subgroup ofC11⋊#15692592, C11⋊#15692591, C11⋊((C7⋊C9)⋊#261), …
maximal quotient ofC9×C7⋊(C11⋊#261), C32×C7⋊(C11⋊#261), C3×C3⋊(C7⋊(C11⋊#261))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 127);