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C32×D251⋊C5 #36377221

order22590
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×D251⋊C5
unambiguous semidirect productD251⋊(C32×C5)
unambiguous semidirect product(C251⋊C5)⋊(C2×C32)
unambiguous semidirect product(C3×D251)⋊(C3×C5)
unambiguous semidirect product(C32×D251)⋊C5

Splittings

Fitting, socle, HallC32×C251 ⋊ C2×C5
derived, SylowC251 ⋊ C2×C32×C5
HallC32×C251⋊C5 ⋊ C2
HallC32×D251 ⋊ C5
HallC251⋊C5 ⋊ C2×C32
HallD251 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32D251⋊C5
commutator, cosocle, hypocenterC251C2×C32×C5
FrattiniC1G
Fitting, socleC32×C251C2×C5
LCSG ▷ C251
UCSC1 ◁ C32

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2259

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22590, 14);