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C4×#65793 #13033427

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#65793

Splittings

FittingC4×C5×#41 ⋊ C4
SylowC5 ⋊ C4×#417

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×#41C4
socleC22×C5C22×C22⋊C4
prime radicalC2×D5×#41C22
cosocleC2×C4×D5C24
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C4×#417
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

1706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72269239
maximal normal subgroup of#72269239

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103695);