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C4×#65721 #13033573

order1280
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#65721

Splittings

FittingC2×C4×C5×C8 ⋊ C4
SylowC5 ⋊ C4×#427

Subgroups

subgroupG/H
centerC42C4⋊AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC22×C5C22×C4⋊C4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C4×#427
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103841);