Finite Group Databasebeta

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C2×C9×C251⋊C5 #36377209

order22590
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C251⋊C5
unambiguous semidirect product(C2×C251)⋊(C5×C9)
unambiguous semidirect product(C2×C9×C251)⋊C5

Splittings

Fitting, HallC2×C9×C251 ⋊ C5
derived, SylowC251 ⋊ C2×C5×C9
HallC9×C251 ⋊ C2×C5
HallC2×C251 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C251⋊C5
commutator, hypocenterC251C2×C5×C9
FrattiniC3C2×C3×C251⋊C5
FittingC2×C9×C251C5
socleC2×C3×C251C3×C5
prime radicalC2×C3×C251⋊C5C3
cosocleC3×C251C2×C3×C5
LCSG ▷ C251
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4518

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22590, 2);