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C11×C7⋊#90866 #49114884

order36036
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C7⋊#90866
unambiguous semidirect productC7⋊(C11×#90866)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC32×C7×C13 ⋊ C4×C11
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ #157
HallC32×C7×C11 ⋊ #261
HallC11×C13 ⋊ C7⋊#157
HallC32×C13 ⋊ C11×Dic7
HallC32×C11 ⋊ C7⋊#261
HallC7×C13 ⋊ C11×#157
HallC7×C11 ⋊ #90866
HallC32×C7 ⋊ C11×#261
SylowC13 ⋊ C11×C7⋊#157
SylowC32 ⋊ C11×C7⋊#261
SylowC7 ⋊ C11×#90866

Subgroups

subgroupG/H
center, hypercenterC11C7⋊#90866
commutator, hypocenterC32×C7×C13C4×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC7×C11×C3⋊D39C2
cosocleC7×C3⋊D39C2×C11
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

2343 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 552);