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AGL(1,𝔽5)×#237 #11756844

order960
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#237

Splittings

FittingC3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C4×#41
SylowC5 ⋊ C4×#237
SylowC3 ⋊ #41×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC2C22×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C23×C4
FittingC3×C5×D4C2×C4
prime radicalD5×#237C2
cosocleC2×C3×D5C24
hypercenterD4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ D4

620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#912, AGL(1,𝔽5)×#916, #14416633, …
maximal normal subgroup ofAGL(1,𝔽5)×#912, AGL(1,𝔽5)×#916, #14416633, …
maximal quotient ofAGL(1,𝔽5)×#877, AGL(1,𝔽5)×#892, AGL(1,𝔽5)×#67⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11039);