Finite Group Databasebeta

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C2×C5×C9×D131 #37556063

order23580
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D131

Splittings

FittingC2×C5×C9×C131 ⋊ C2
derived, SylowC131 ⋊ C22×C5×C9
HallC5×C9×C131 ⋊ C22
HallC9×C131 ⋊ C22×C5
HallC5×C131 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D131
commutator, hypocenterC131C22×C5×C9
FrattiniC3C2×C3×C5×D131
FittingC2×C5×C9×C131C2
socleC2×C3×C5×C131C2×C3
prime radicalC2×C3×C5×D131C3
cosocleC3×C131C22×C3×C5
LCSG ▷ C131
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11790

Conjugacy classes & character table

6030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 38);