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ΓL(1,𝔽32)×C3⋊D39 #49136607

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

Aliases

direct productΓL(1,𝔽32)×C3⋊D39
unambiguous semidirect productC3⋊(D39×ΓL(1,𝔽32))
unambiguous semidirect productC13⋊(C3⋊D3×ΓL(1,𝔽32))
unambiguous semidirect product(C31×C3⋊D39)⋊C5

Splittings

Fitting, socle, derived, HallC32×C13×C31 ⋊ C2×C5
HallC32×C13×ΓL(1,𝔽32) ⋊ C2
HallC31×C3⋊D39 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3⋊D3
HallC32×ΓL(1,𝔽32) ⋊ D13
HallC13×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ C5×D13
HallC32×C13 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C3⋊D39
SylowC13 ⋊ C3⋊D3×ΓL(1,𝔽32)
SylowC32 ⋊ D13×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C13×C31C2×C5
LCSG ▷ C32×C13×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3627

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 127);