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ΓL(1,𝔽32)×D119 #49146275

order36890
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽32)×D119
unambiguous semidirect productC7⋊(D17×ΓL(1,𝔽32))
unambiguous semidirect productC17⋊(D7×ΓL(1,𝔽32))
unambiguous semidirect product(C31×D119)⋊C5

Splittings

Fitting, socle, derived, HallC7×C17×C31 ⋊ C2×C5
HallC7×C17×ΓL(1,𝔽32) ⋊ C2
HallC31×D119 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ D7
HallC7×ΓL(1,𝔽32) ⋊ D17
HallC17×C31 ⋊ C5×D7
HallC7×C31 ⋊ C5×D17
HallC7×C17 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D119
SylowC17 ⋊ D7×ΓL(1,𝔽32)
SylowC7 ⋊ D17×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C17×C31C2×C5
LCSG ▷ C7×C17×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 23);