Finite Group Databasebeta

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C4×#65276 #12020516

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4×#65276

Splittings

FittingC2×C4×C5×C4⋊C4 ⋊ C2
SylowC5 ⋊ C4×#380

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C22×C42
FrattiniC24C23×D5
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C4×#380
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 90784);