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AGL(1,𝔽5)×#340 #13021590

order1280
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productAGL(1,𝔽5)×#340

Splittings

FittingC5×#340 ⋊ C4
SylowC5 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23D4×AGL(1,𝔽5)
commutatorC4×C5C43
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#340C4
socleC23×C5C4×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×D5C23
hypercenter#340AGL(1,𝔽5)
hypocenterC5C4×#340
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1091858);