Finite Group Databasebeta

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C2×C9×C401⋊C5 #49115387

order36090
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C401⋊C5
unambiguous semidirect product(C2×C401)⋊(C5×C9)
unambiguous semidirect product(C2×C9×C401)⋊C5

Splittings

Fitting, HallC2×C9×C401 ⋊ C5
derived, SylowC401 ⋊ C2×C5×C9
HallC9×C401 ⋊ C2×C5
HallC2×C401 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C401⋊C5
commutator, hypocenterC401C2×C5×C9
FrattiniC3C2×C3×C401⋊C5
FittingC2×C9×C401C5
socleC2×C3×C401C3×C5
prime radicalC2×C3×C401⋊C5C3
cosocleC3×C401C2×C3×C5
LCSG ▷ C401
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7218

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36090, 2);