Finite Group Databasebeta

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C11×C3⋊(C3⋊(C7⋊#261)) #49114976

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

Aliases

direct productC11×C3⋊(C3⋊(C7⋊#261))
unambiguous semidirect productC3⋊(C11×C3⋊(C7⋊#261))
unambiguous semidirect productC7⋊(C11×C3⋊(C3⋊#261))

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC32×C7×C13 ⋊ C4×C11
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ C3⋊Dic3
HallC32×C7×C11 ⋊ #261
HallC11×C13 ⋊ C3⋊Dic21
HallC32×C13 ⋊ C11×Dic7
HallC32×C11 ⋊ C7⋊#261
HallC7×C13 ⋊ C11×C3⋊Dic3
HallC7×C11 ⋊ C3⋊(C3⋊#261)
HallC32×C7 ⋊ C11×#261
SylowC13 ⋊ C11×C3⋊Dic21
SylowC32 ⋊ C11×C7⋊#261
SylowC7 ⋊ C11×C3⋊(C3⋊#261)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C3⋊(C7⋊#261))
commutator, hypocenterC32×C7×C13C4×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC32×C7×D13C2×C11
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

2805 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 644);