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M32×ΓL(1,𝔽16) #14312588

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productM32×ΓL(1,𝔽16)

Splittings

FittingC3×C5×M32 ⋊ C4
HallC3×C5 ⋊ C4×M32
SylowC5 ⋊ Dic3×M32
SylowC3 ⋊ AGL(1,𝔽5)×M32

Subgroups

subgroupG/H
center, FrattiniC8C22×ΓL(1,𝔽16)
commutator, socleC2×C3×C5C2×C4×C8
FittingC3×C5×M32C4
prime radicalC22×C3×D5C2×C8
cosocleC3×C8×D5C23
hypercenterM32ΓL(1,𝔽16)
hypocenterC3×C5C4×M32
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C8 ◁ M32

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38286);