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C2×C3×D631⋊C3 #36384283

order22716
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D631⋊C3
unambiguous semidirect productD631⋊(C2×C32)
unambiguous semidirect product(C631⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D631)⋊C32
unambiguous semidirect product(C2×C631⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D631)⋊C3

Splittings

Fitting, socleC2×C3×C631 ⋊ C2×C3
derived, SylowC631 ⋊ C22×C32
HallC3×C631⋊C3 ⋊ C22
HallC2×D631 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D631⋊C3
commutator, cosocle, hypocenterC631C22×C32
FrattiniC1G
Fitting, socleC2×C3×C631C2×C3
LCSG ▷ C631
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3786

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22716, 34);