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AGL(1,𝔽5)×#453 #13036190

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽5)×#453

Splittings

FittingC5×#453 ⋊ C4
SylowC5 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#120
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#453C4
socleC2×C5C4×#120
prime radicalD5×#453C2
cosocleC2×C4×D5C24
hypercenter#453AGL(1,𝔽5)
hypocenterC5C4×#453
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

1578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 40

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#5935, #72213584, #453×#1043, …
maximal normal subgroup ofAGL(1,𝔽5)×#3019, C2×AGL(1,𝔽5)×#453, AGL(1,𝔽5)×#3292, …
maximal quotient of#72213584, #453×#1043, AGL(1,𝔽5)×#2002, …
holomorph ofC5×D4

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1106458);