Finite Group Databasebeta

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D13⋊C3×(C31⋊C3)⋊C5 #49136555

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productD13⋊C3×(C31⋊C3)⋊C5
unambiguous semidirect product(C13⋊C3)⋊(C2×(C31⋊C3)⋊C5)
unambiguous semidirect product(D13⋊C3×C31⋊C3)⋊C5
unambiguous semidirect product(D13×(C31⋊C3)⋊C5)⋊C3
unambiguous semidirect product(D13⋊C3×ΓL(1,𝔽32))⋊C3
unambiguous semidirect product(#14559026⋊C5)⋊C3
unambiguous semidirect product(#14559027⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C32×C5
HallC13⋊C3×(C31⋊C3)⋊C5 ⋊ C2
HallD13⋊C3×C31⋊C3 ⋊ C5
HallD13×ΓL(1,𝔽32) ⋊ C32
HallC13⋊C3×C31⋊C3 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallD13×C31 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×D13⋊C3
SylowC31 ⋊ C3×C5×D13⋊C3
HallD13 ⋊ C3×(C31⋊C3)⋊C5
SylowC13 ⋊ C2×C3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C31C2×C32×C5
LCSG ▷ C13×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 403

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 75);