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AGL(1,𝔽5)×#430 #13033598

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×#430

Splittings

FittingC5×#430 ⋊ C4
SylowC5 ⋊ C4×#430

Subgroups

subgroupG/H
centerC4C2×D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#430C4
socleC2×C5C2×C4×C4⋊C4
prime radicalC23×D5C2×Q8
cosocleC2×C4×D5C24
hypercenter#430AGL(1,𝔽5)
hypocenterC5C4×#430
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

1034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2956, AGL(1,𝔽5)×#3068, #72226385, …
maximal normal subgroup ofAGL(1,𝔽5)×#2956, AGL(1,𝔽5)×#3068, AGL(1,𝔽5)×#2238
maximal quotient of#72226385, #72226573

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103866);