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C22×M16×AGL(1,𝔽5) #13044380

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×M16×AGL(1,𝔽5)

Splittings

FittingC22×C5×M16 ⋊ C4
SylowC5 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC4C24×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC23×C5C2×C42
prime radicalC24×D5C2×C4
cosocleC4×D5C25
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C22×C4×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×M16

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×#13103905, C2×AGL(1,𝔽5)×#568
maximal normal subgroup ofC2×AGL(1,𝔽5)×#568
maximal quotient ofC22×AGL(1,𝔽5)×#97, C22×#13103905, AGL(1,𝔽5)×#2970

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114648);