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C3×C11×C7⋊#261 #26046535

order12012
isoclinismisoclinic class of C7⋊#261
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C7⋊#261

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C11C7⋊#261
commutator, hypocenterC7×C13C3×C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C4
prime radicalC3×C7×C11×D13C2
cosocleC7×D13C2×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1023 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×C11×C7⋊#261, C32×C11×C7⋊#261, C3×C11×C3⋊(C7⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 125);