Finite Group Databasebeta

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C4×#64869 #13017025

order1280
isoclinismisoclinic class of #64868
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#64869

Splittings

FittingC4×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ C4×#328

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C2×D4
cosocleC22×C4×D5C23
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5C4×#328
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087293);