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AGL(1,𝔽5)×#812 #14312614

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

Aliases

direct productAGL(1,𝔽5)×#812

Splittings

HallC3×C5 ⋊ C4×M32
SylowC5 ⋊ C4×#812
SylowC3 ⋊ AGL(1,𝔽5)×M32

Subgroups

subgroupG/H
center, FrattiniC8C2×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C2×C4×C8
FittingC2×C3×C5×C8C2×C4
prime radicalC22×C3×D5C2×C8
cosocleC3×C8×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×M32
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C8 ◁ C2×C8

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, 38312);