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D13×C3⋊(D31⋊C5) #37563806

order24180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD13×C3⋊(D31⋊C5)
unambiguous semidirect product(C3×D13)⋊(D31⋊C5)
unambiguous semidirect product(D13×ΓL(1,𝔽32))⋊D3
unambiguous semidirect product(D13×D93)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C31 ⋊ C22×C5
HallC3×C13×ΓL(1,𝔽32) ⋊ C22
HallD13×D93 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×D13
HallC13×C31 ⋊ C2×C5×D3
HallΓL(1,𝔽32) ⋊ D3×D13
HallC3×C31 ⋊ C2×C5×D13
HallC3×C13 ⋊ C2×D31⋊C5
SylowC31 ⋊ C5×D3×D13
SylowC13 ⋊ C2×C3⋊(D31⋊C5)
SylowC3 ⋊ D13×D31⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C31C22×C5
LCSG ▷ C3×C13×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1209

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 105);