Finite Group Databasebeta

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Dic9×C131⋊C5 #37556036

order23580
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productDic9×C131⋊C5
unambiguous semidirect productC9⋊(C4×C131⋊C5)
unambiguous semidirect product(Dic9×C131)⋊C5

Splittings

derived, HallC9×C131 ⋊ C4×C5
HallC9×C131⋊C5 ⋊ C4
HallDic9×C131 ⋊ C5
SylowC131 ⋊ C5×Dic9
SylowC9 ⋊ C4×C131⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D9×C131⋊C5
commutator, hypocenterC9×C131C4×C5
FrattiniC2×C3D3×C131⋊C5
Fitting, cosocleC2×C9×C131C2×C5
socleC2×C3×C131C5×D3
prime radicalC2×C3×C131⋊C5D3
LCSG ▷ C9×C131
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4716

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 11);