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C4×#65727 #13033580

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#65727

Splittings

FittingC4×C5×M16 ⋊ C4
SylowC5 ⋊ C4×#428

Subgroups

subgroupG/H
centerC2×C4C2×C4⋊AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×M16C4
socleC22×C5C22×C4⋊C4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenterC4×M16AGL(1,𝔽5)
hypocenterC5C4×#428
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

1218 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#72269215
maximal normal subgroup of#72269215

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103848);