Finite Group Databasebeta

← Prev (#49114967) Next (#49114969) →

C7×C11×C3⋊(C3⋊#261) #49114968

order36036
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC32×C13 ⋊ C4×C7×C11
HallC32×C11×C13 ⋊ C4×C7
HallC7×C11×C13 ⋊ C3⋊Dic3
HallC32×C7×C13 ⋊ C4×C11
HallC32×C7×C11 ⋊ #261
HallC11×C13 ⋊ C7×C3⋊Dic3
HallC32×C11 ⋊ C7×#261
HallC7×C13 ⋊ C11×C3⋊Dic3
HallC32×C7 ⋊ C11×#261
SylowC13 ⋊ C7×C11×C3⋊Dic3
SylowC32 ⋊ C7×C11×#261

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊(C3⋊#261)
commutator, hypocenterC32×C13C4×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC32×D13C2×C7×C11
LCSG ▷ C32×C13
UCSC1 ◁ C7×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 636);