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C13×(C11⋊C5)⋊#157 #38788018

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×(C11⋊C5)⋊#157
unambiguous semidirect product(C11⋊C5)⋊(C13×#157)
unambiguous semidirect product(C11⋊#157)⋊(C5×C13)
unambiguous semidirect product(C13×C11⋊#157)⋊C5

Splittings

Fitting, socle, HallC32×C11×C13 ⋊ C4×C5
derived, HallC32×C11 ⋊ C4×C5×C13
HallC32×C13×C11⋊C5 ⋊ C4
HallC13×C11⋊#157 ⋊ C5
HallC13×C11⋊C5 ⋊ #157
HallC32×C11⋊C5 ⋊ C4×C13
HallC11⋊#157 ⋊ C5×C13
HallC11×C13 ⋊ C5×#157
HallC32×C13 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C13×#157
SylowC11 ⋊ C5×C13×#157
SylowC32 ⋊ C13×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC13(C11⋊C5)⋊#157
commutator, hypocenterC32×C11C4×C5×C13
FrattiniC1G
Fitting, socleC32×C11×C13C4×C5
prime radicalC13×C3⋊D3×C11⋊C5C2
cosocleC11×C3⋊D3C2×C5×C13
LCSG ▷ C32×C11
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 858

Conjugacy classes & character table

468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 249);