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D3×C13×(C31⋊C3)⋊C5 #49136571

order36270
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productD3×C13×(C31⋊C3)⋊C5
unambiguous semidirect productC3⋊(C2×C13×(C31⋊C3)⋊C5)
unambiguous semidirect product(D3×C31⋊C3)⋊(C5×C13)
unambiguous semidirect product(D3×ΓL(1,𝔽32))⋊(C3×C13)
unambiguous semidirect product(D3×C13×C31⋊C3)⋊C5

Splittings

Fitting, socleC3×C13×C31 ⋊ C2×C3×C5
derivedC3×C31 ⋊ C2×C3×C5×C13
HallC3×C13×(C31⋊C3)⋊C5 ⋊ C2
HallD3×C13×C31⋊C3 ⋊ C5
HallC3×C13×C31⋊C3 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×(C31⋊C3)⋊C5 ⋊ C2×C13
HallD3×C31⋊C3 ⋊ C5×C13
HallC13×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C2×C5×C13
HallΓL(1,𝔽32) ⋊ C3×D3×C13
SylowC31 ⋊ C3×C5×D3×C13

Subgroups

subgroupG/H
center, hypercenterC13D3×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1209

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 91);