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C22×C4×C22⋊AGL(1,𝔽5) #13043824

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×C4×C22⋊AGL(1,𝔽5)

Splittings

FittingC24×C4×C5 ⋊ C4
SylowC5 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC22C24×AGL(1,𝔽5)
FittingC24×C4×C5C4
socleC24×C5C22×C4
prime radicalC25×D5C22
cosocleC22×D5C25
hypercenterC24×C4AGL(1,𝔽5)
hypocenterC5C22×C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C24×C4

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114092);