Finite Group Databasebeta

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C5×C9⋊#10596816 #39907946

order26100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊#10596816
unambiguous semidirect productC9⋊(C5×#10596816)

Splittings

Fitting, HallC52×C9×C29 ⋊ C4
derivedC5×C9×C29 ⋊ C4×C5
HallC52×C29 ⋊ Dic9
HallC9×C29 ⋊ C5×AGL(1,𝔽5)
HallC52×C9 ⋊ Dic29
SylowC29 ⋊ C5×C9⋊AGL(1,𝔽5)
SylowC52 ⋊ Dic261
SylowC9 ⋊ C5×#10596816

Subgroups

subgroupG/H
center, hypercenterC5C9⋊#10596816
commutator, hypocenterC5×C9×C29C4×C5
FrattiniC3C5×C3⋊#10596816
FittingC52×C9×C29C4
socleC3×C52×C29Dic3
prime radicalC3×C5×D5×C29D3
cosocleC9×D5×C29C2×C5
LCSG ▷ C5×C9×C29
UCSC1 ◁ C5

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 180);