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C4×#65701 #13033116

order1280
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC4×#65701

Splittings

SylowC5 ⋊ C4×#405

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C2×C43
FrattiniC23C23×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5C4×#405
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103384);