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C4×#64920 #13017018

order1280
isoclinismisoclinic class of #64868
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#64920

Splittings

FittingC2×C4×C5×D4 ⋊ C4
SylowC5 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC23×C5C2×C22⋊C4
prime radicalC2×#4084C22
cosocleC22×C4×D5C23
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C4×#327
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

816 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, 1087286);