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C2×C13×D241⋊C3 #49178121

order37596
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D241⋊C3
unambiguous semidirect productD241⋊(C2×C3×C13)
unambiguous semidirect product(C241⋊C3)⋊(C22×C13)
unambiguous semidirect product(C2×D241)⋊(C3×C13)
unambiguous semidirect product(C2×C241⋊C3)⋊(C2×C13)

Splittings

Fitting, socleC2×C13×C241 ⋊ C2×C3
derived, SylowC241 ⋊ C22×C3×C13
HallC2×C13×D241 ⋊ C3
HallC13×C241⋊C3 ⋊ C22
HallC13×C241 ⋊ C22×C3
HallC2×D241 ⋊ C3×C13
HallC241⋊C3 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D241⋊C3
commutator, cosocle, hypocenterC241C22×C3×C13
FrattiniC1G
Fitting, socleC2×C13×C241C2×C3
LCSG ▷ C241
UCSC1 ◁ C2×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6266

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37596, 54);