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AGL(1,𝔽5)×#525 #13043874

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#525

Splittings

FittingC5×#525 ⋊ C4
SylowC5 ⋊ C4×#525

Subgroups

subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC5×#525C4
prime radicalD5×#525C2
cosocleC22×D5C25
hypercenter#525AGL(1,𝔽5)
hypocenterC5C4×#525
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #525

3902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#525×#1043, AGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#1891, …
maximal normal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#1891, AGL(1,𝔽5)×#3003, …
maximal quotient of#525×#1043, #72221683, #72226493, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114142);