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ΓL(1,𝔽32)×D87 #41004206

order26970
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽32)×D87
unambiguous semidirect productC3⋊(D29×ΓL(1,𝔽32))
unambiguous semidirect productC29⋊(D3×ΓL(1,𝔽32))
unambiguous semidirect product(C31×D87)⋊C5

Splittings

Fitting, socle, derived, HallC3×C29×C31 ⋊ C2×C5
HallC3×C29×ΓL(1,𝔽32) ⋊ C2
HallC31×D87 ⋊ C5
HallC29×ΓL(1,𝔽32) ⋊ D3
HallC29×C31 ⋊ C5×D3
HallC3×ΓL(1,𝔽32) ⋊ D29
HallC3×C31 ⋊ C5×D29
HallC3×C29 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D87
SylowC29 ⋊ D3×ΓL(1,𝔽32)
SylowC3 ⋊ D29×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C29×C31C2×C5
LCSG ▷ C3×C29×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 25);