Finite Group Databasebeta

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C5×C9⋊#66772 #29505795

order15300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊#66772
unambiguous semidirect productC9⋊(C5×#66772)

Splittings

Fitting, HallC52×C9×C17 ⋊ C4
derivedC5×C9×C17 ⋊ C4×C5
HallC52×C17 ⋊ Dic9
HallC52×C9 ⋊ #595
HallC9×C17 ⋊ C5×Dic5
SylowC52 ⋊ C9⋊#595
SylowC17 ⋊ C5×Dic45
SylowC9 ⋊ C5×#66772

Subgroups

subgroupG/H
center, hypercenterC5C9⋊#66772
commutator, hypocenterC5×C9×C17C4×C5
FrattiniC3C5×C3⋊#66772
FittingC52×C9×C17C4
socleC3×C52×C17Dic3
prime radicalC3×C52×D17D3
cosocleC5×C9×D17C2×C5
LCSG ▷ C5×C9×C17
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1530

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 181);