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AGL(1,𝔽5)×#948 #14411503

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×#948

Splittings

HallC3×C5 ⋊ C4×#131
SylowC5 ⋊ C4×#948
SylowC3 ⋊ AGL(1,𝔽5)×#131

Subgroups

subgroupG/H
center, FrattiniC4C22×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C22×C42
FittingC3×C5×#41C2×C4
prime radicalC3×D5×#41C22
cosocleC3×C4×D5C24
hypercenter#41D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#131
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ #41

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137201);