Finite Group Databasebeta

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C5×C9×#66774 #29505770

order15300
isoclinismisoclinic class of #66774
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×#66774

Splittings

Fitting, HallC52×C9×C17 ⋊ C4
derivedC5×C17 ⋊ C4×C5×C9
HallC52×C17 ⋊ C4×C9
HallC52×C9 ⋊ Dic17
HallC9×C17 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ C9×Dic17
SylowC17 ⋊ C5×C9×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5×C9#66774
commutator, hypocenterC5×C17C4×C5×C9
FrattiniC3C3×C5×#66774
FittingC52×C9×C17C4
socleC3×C52×C17C3×C4
prime radicalC3×C5×D5×C17C2×C3
cosocleC3×D5×C17C2×C3×C5
LCSG ▷ C5×C17
UCSC1 ◁ C5×C9

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3060

Conjugacy classes & character table

1665 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 156);