Finite Group Databasebeta

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C2×C5×C9×D149 #41001250

order26820
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D149
unambiguous semidirect productC149⋊(C22×C5×C9)
unambiguous semidirect product(C2×C149)⋊(C2×C5×C9)

Splittings

FittingC2×C5×C9×C149 ⋊ C2
derived, SylowC149 ⋊ C22×C5×C9
HallC5×C9×C149 ⋊ C22
HallC9×C149 ⋊ C22×C5
HallC5×C149 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D149
commutator, hypocenterC149C22×C5×C9
FrattiniC3C2×C3×C5×D149
FittingC2×C5×C9×C149C2
socleC2×C3×C5×C149C2×C3
prime radicalC2×C3×C5×D149C3
cosocleC3×C149C22×C3×C5
LCSG ▷ C149
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13410

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 36);