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AGL(1,𝔽5)×#365 #13026028

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

Aliases

direct productAGL(1,𝔽5)×#365

Splittings

FittingC5×#365 ⋊ C4
SylowC5 ⋊ C4×#365

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#106
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#365C4
socleC2×C5C4×#106
prime radicalC22×D5C2×SD16
cosocleC2×C8×D5C23
hypercenter#365AGL(1,𝔽5)
hypocenterC5C4×#365
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), #72220749, AGL(1,𝔽5)×#2230, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), AGL(1,𝔽5)×#2230, C2×AGL(1,𝔽5)×#365, …
maximal quotient of#72220749, AGL(1,𝔽5)×#1368, #365×#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1096296);