Finite Group Databasebeta

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C5×C13×#261⋊C9 #44477612

order30420
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×#261⋊C9
unambiguous semidirect product#261⋊(C5×C9×C13)
unambiguous semidirect product(C5×#261)⋊(C9×C13)

Splittings

derivedC13 ⋊ C4×C5×C9×C13
HallC5×C13×C13⋊C9 ⋊ C4
HallC5×C13×#261 ⋊ C9
HallC13×C13⋊C9 ⋊ C4×C5
HallC5×C132 ⋊ C4×C9
HallC13×#261 ⋊ C5×C9
SylowC132 ⋊ C4×C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13AGL(1,𝔽13)
commutator, hypocenterC13C4×C5×C9×C13
FrattiniC3C5×C13×AGL(1,𝔽13)
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×C5×C13×D13C2×C3
cosocleC3×D13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C3×C5×C13

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

2535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 201);