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AGL(1,𝔽5)×#417 #13033428

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productAGL(1,𝔽5)×#417

Splittings

FittingC5×#417 ⋊ C4
SylowC5 ⋊ C4×#417

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#417C4
socleC22×C5C2×C4×D4
prime radicalC2×D5×#41C22
cosocleC2×C4×D5C24
hypercenter#417AGL(1,𝔽5)
hypocenterC5C4×#417
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

1706 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)×#3060, AGL(1,𝔽5)×#1792, AGL(1,𝔽5)×#2952, …
maximal normal subgroup ofAGL(1,𝔽5)×#3060, AGL(1,𝔽5)×#1792, AGL(1,𝔽5)×#2952, …
maximal quotient ofAGL(1,𝔽5)×#1504, #72253329

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103696);