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AGL(1,𝔽5)×#357 #13025873

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productAGL(1,𝔽5)×#357

Splittings

FittingC5×#357 ⋊ C4
SylowC5 ⋊ C4×#357

Subgroups

subgroupG/H
centerC22D8×AGL(1,𝔽5)
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#357C4
socleC22×C5C4×D8
prime radicalC2×D5×D8C22
cosocleC2×C8×D5C23
hypercenter#357AGL(1,𝔽5)
hypocenterC5C4×#357
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2177, #357×#1043
maximal normal subgroup ofAGL(1,𝔽5)×#2177
maximal quotient ofAGL(1,𝔽5)×#1419, AGL(1,𝔽5)×#1418, #357×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1096141);