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C13×C7⋊(C11⋊#157) #49114886

order36036
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×C7⋊(C11⋊#157)
unambiguous semidirect productC7⋊(C13×C11⋊#157)
unambiguous semidirect productC11⋊(C13×C7⋊#157)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC32×C7×C11 ⋊ C4×C13
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ #157
HallC32×C7×C13 ⋊ Dic11
HallC11×C13 ⋊ C7⋊#157
HallC32×C13 ⋊ Dic77
HallC32×C11 ⋊ C13×Dic7
HallC7×C13 ⋊ C11⋊#157
HallC7×C11 ⋊ C13×#157
HallC32×C7 ⋊ C13×Dic11
SylowC11 ⋊ C13×C7⋊#157
SylowC32 ⋊ C13×Dic77
SylowC7 ⋊ C13×C11⋊#157

Subgroups

subgroupG/H
center, hypercenterC13C7⋊(C11⋊#157)
commutator, hypocenterC32×C7×C11C4×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC7×C11×C13×C3⋊D3C2
cosocleC7×C11×C3⋊D3C2×C13
LCSG ▷ C32×C7×C11
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

3042 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 554);