Finite Group Databasebeta

← Prev (#49115023) Next (#49115025) →

C2×C7×C11×C13×C3⋊D3 #49115024

order36036
automorphism?
homologyAbelianization (H1) = C22×C7×C11×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C11×C13×C3⋊D3
unambiguous semidirect product(C2×C3)⋊(D3×C7×C11×C13)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, SylowC32 ⋊ C22×C7×C11×C13
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C7
HallC32×C7×C13 ⋊ C22×C11
HallC32×C7×C11 ⋊ C22×C13
HallC32×C13 ⋊ C22×C7×C11
HallC32×C11 ⋊ C22×C7×C13
HallC32×C7 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11×C13C3⋊D3
commutator, cosocle, hypocenterC32C22×C7×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32
UCSC1 ◁ C2×C7×C11×C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

12012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 692);