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C5×C37×AGL(1,𝔽13) #43274146

order28860
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C37×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C5×C37)
unambiguous semidirect product(C5×#261)⋊(C3×C37)

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C5×C37
HallC5×C37×#261 ⋊ C3
HallC5×C37×C13⋊C3 ⋊ C4
HallC37×#261 ⋊ C3×C5
HallC37×C13⋊C3 ⋊ C4×C5
HallC13×C37 ⋊ C3×C4×C5
HallC5×#261 ⋊ C3×C37
HallC5×C13⋊C3 ⋊ C4×C37
HallC5×C13 ⋊ C3×C4×C37
Hall#261 ⋊ C3×C5×C37
HallC13⋊C3 ⋊ C4×C5×C37

Subgroups

subgroupG/H
center, hypercenterC5×C37AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C5×C37
FrattiniC1G
Fitting, socleC5×C13×C37C3×C4
prime radicalC5×C37×D13⋊C3C2
cosocleD13C2×C3×C5×C37
LCSG ▷ C13
UCSC1 ◁ C5×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

2405 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 51);