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C37×C3⋊(D31⋊C5) #46806201

order34410
automorphism?
homologyAbelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×C3⋊(D31⋊C5)
unambiguous semidirect productC3⋊(C37×D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(D3×C37)
unambiguous semidirect productD93⋊(C5×C37)
unambiguous semidirect product(C37×D93)⋊C5

Splittings

Fitting, socle, HallC3×C31×C37 ⋊ C2×C5
derived, HallC3×C31 ⋊ C2×C5×C37
HallC3×C37×ΓL(1,𝔽32) ⋊ C2
HallC37×D93 ⋊ C5
HallC37×ΓL(1,𝔽32) ⋊ D3
HallC31×C37 ⋊ C5×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×C37
HallD93 ⋊ C5×C37
HallΓL(1,𝔽32) ⋊ D3×C37
HallC3×C37 ⋊ D31⋊C5
SylowC31 ⋊ C5×D3×C37
SylowC3 ⋊ C37×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC37C3⋊(D31⋊C5)
commutator, cosocle, hypocenterC3×C31C2×C5×C37
FrattiniC1G
Fitting, socleC3×C31×C37C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3441

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 31);