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AGL(1,𝔽5)×#349 #13025684

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productAGL(1,𝔽5)×#349

Splittings

FittingC5×#349 ⋊ C4
SylowC5 ⋊ C4×#349

Subgroups

subgroupG/H
centerC4C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C2×C4×C8
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#349C4
socleC2×C5C4×C22⋊C8
prime radicalC23×D5C2×C8
cosocleC2×C8×D5C23
hypercenter#349AGL(1,𝔽5)
hypocenterC5C4×#349
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #349

522 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)×#2165, AGL(1,𝔽5)×#2190, AGL(1,𝔽5)×#2238
maximal normal subgroup ofAGL(1,𝔽5)×#2165, AGL(1,𝔽5)×#2190, AGL(1,𝔽5)×#2238

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095952);