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C7×C11⋊#90865 #49114882

order36036
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C11⋊#90865
unambiguous semidirect productC11⋊(C7×#90865)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC32×C11×C13 ⋊ C4×C7
HallC7×C11×C13 ⋊ #157
HallC32×C7×C13 ⋊ Dic11
HallC32×C7×C11 ⋊ Dic13
HallC11×C13 ⋊ C7×#157
HallC32×C13 ⋊ C7×Dic11
HallC32×C11 ⋊ C7×Dic13
HallC7×C13 ⋊ C11⋊#157
HallC7×C11 ⋊ #90865
HallC32×C7 ⋊ Dic143
SylowC13 ⋊ C7×C11⋊#157
SylowC11 ⋊ C7×#90865
SylowC32 ⋊ C7×Dic143

Subgroups

subgroupG/H
center, hypercenterC7C11⋊#90865
commutator, hypocenterC32×C11×C13C4×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC7×C11×C13×C3⋊D3C2
cosocleC11×C13×C3⋊D3C2×C7
LCSG ▷ C32×C11×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

3024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 550);