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ΓL(1,𝔽32)×D111 #46806200

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

Aliases

direct productΓL(1,𝔽32)×D111
unambiguous semidirect productC3⋊(D37×ΓL(1,𝔽32))
unambiguous semidirect productC37⋊(D3×ΓL(1,𝔽32))
unambiguous semidirect product(C31×D111)⋊C5

Splittings

Fitting, socle, derived, HallC3×C31×C37 ⋊ C2×C5
HallC3×C37×ΓL(1,𝔽32) ⋊ C2
HallC31×D111 ⋊ C5
HallC37×ΓL(1,𝔽32) ⋊ D3
HallC31×C37 ⋊ C5×D3
HallC3×ΓL(1,𝔽32) ⋊ D37
HallC3×C37 ⋊ C2×ΓL(1,𝔽32)
HallC3×C31 ⋊ C5×D37
SylowC37 ⋊ D3×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D111
SylowC3 ⋊ D37×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C31×C37C2×C5
LCSG ▷ C3×C31×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3441

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 30);