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C4×#64899 #13021617

order1280
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#64899

Splittings

FittingC4×C5×M16 ⋊ C4
SylowC5 ⋊ C4×#343

Subgroups

subgroupG/H
centerC2×C4(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C5C43
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×M16C4
socleC22×C5C2×#95
prime radicalC23×D5C22×C4
cosocleC22×C4×D5C23
hypercenterC4×M16AGL(1,𝔽5)
hypocenterC5C4×#343
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1091885);