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C7×(C11⋊C5)⋊#157 #28357571

order13860
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×(C11⋊C5)⋊#157
unambiguous semidirect product(C11⋊C5)⋊(C7×#157)
unambiguous semidirect product(C11⋊#157)⋊(C5×C7)
unambiguous semidirect product(C7×C11⋊#157)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C4×C5
derived, HallC32×C11 ⋊ C4×C5×C7
HallC32×C7×C11⋊C5 ⋊ C4
HallC7×C11⋊#157 ⋊ C5
HallC32×C11⋊C5 ⋊ C4×C7
HallC11⋊#157 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ #157
HallC7×C11 ⋊ C5×#157
HallC32×C7 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C7×#157
SylowC11 ⋊ C5×C7×#157
SylowC32 ⋊ C7×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC7(C11⋊C5)⋊#157
commutator, hypocenterC32×C11C4×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C11C4×C5
prime radicalC7×C3⋊D3×C11⋊C5C2
cosocleC11×C3⋊D3C2×C5×C7
LCSG ▷ C32×C11
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 238);