Finite Group Databasebeta

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C2×C5×C9×D137 #37590382

order24660
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D137
unambiguous semidirect productC137⋊(C22×C5×C9)
unambiguous semidirect product(C2×C137)⋊(C2×C5×C9)

Splittings

FittingC2×C5×C9×C137 ⋊ C2
derived, SylowC137 ⋊ C22×C5×C9
HallC5×C9×C137 ⋊ C22
HallC9×C137 ⋊ C22×C5
HallC5×C137 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D137
commutator, hypocenterC137C22×C5×C9
FrattiniC3C2×C3×C5×D137
FittingC2×C5×C9×C137C2
socleC2×C3×C5×C137C2×C3
prime radicalC2×C3×C5×D137C3
cosocleC3×C137C22×C3×C5
LCSG ▷ C137
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12330

Conjugacy classes & character table

6300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24660, 36);