Finite Group Databasebeta

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C32×C7⋊(C11⋊#261) #49114894

order36036
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7⋊(C11⋊#261)
unambiguous semidirect productC11⋊(C32×C7⋊#261)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC7×C11×C13 ⋊ C32×C4
HallC32×C11×C13 ⋊ Dic7
HallC32×C7×C13 ⋊ Dic11
HallC32×C7×C11 ⋊ #261
HallC11×C13 ⋊ C32×Dic7
HallC32×C13 ⋊ Dic77
HallC32×C11 ⋊ C7⋊#261
HallC7×C13 ⋊ C32×Dic11
HallC7×C11 ⋊ C32×#261
HallC32×C7 ⋊ C11⋊#261
SylowC13 ⋊ C32×Dic77
SylowC11 ⋊ C32×C7⋊#261
SylowC7 ⋊ C32×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC32C7⋊(C11⋊#261)
commutator, hypocenterC7×C11×C13C32×C4
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC7×C11×D13C2×C32
LCSG ▷ C7×C11×C13
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

2799 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 562);