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AGL(1,𝔽5)×#912 #14416301

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#912

Splittings

FittingC3×C5×D8 ⋊ C2×C4
HallC3×C5 ⋊ C4×#135
SylowC5 ⋊ C4×#912
SylowC3 ⋊ AGL(1,𝔽5)×#135

Subgroups

subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#912C2
cosocleC3×C4×D5C24
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ D8

1000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141999);