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AGL(1,𝔽5)×#576 #13044750

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

Aliases

direct productAGL(1,𝔽5)×#576

Splittings

FittingC5×#576 ⋊ C4
SylowC5 ⋊ C4×#576

Subgroups

subgroupG/H
centerC2C22×D4×AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC5×#576C4
socleC2×C5C22×C4×D4
prime radicalD5×#576C2
cosocleC4×D5C25
hypercenter#576AGL(1,𝔽5)
hypocenterC5C4×#576
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ #41 ◁ #576

2826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221147, AGL(1,𝔽5)×#3585, AGL(1,𝔽5)×#3292, …
maximal normal subgroup ofAGL(1,𝔽5)×#3585, AGL(1,𝔽5)×#3292, AGL(1,𝔽5)×#3288, …
maximal quotient of#72221147, #72223004, #72223447, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1115018);