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AGL(1,𝔽5)×#493 #13036828

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productAGL(1,𝔽5)×#493

Splittings

FittingC5×#493 ⋊ C4
SylowC5 ⋊ C4×#493

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#493C4
socleC22×C5C2×C4×D4
prime radicalD5×#493C2
cosocleC2×C4×D5C24
hypercenter#493AGL(1,𝔽5)
hypocenterC5C4×#493
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #493

1422 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 of#493×#1043, AGL(1,𝔽5)×#3151, AGL(1,𝔽5)×#1712, …
maximal normal subgroup ofAGL(1,𝔽5)×#3151, AGL(1,𝔽5)×#1712, AGL(1,𝔽5)×#1721, …
maximal quotient of#493×#1043, AGL(1,𝔽5)×#1712, AGL(1,𝔽5)×#1721, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1107096);