Finite Group Databasebeta

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C4×#64750 #12004506

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

Aliases

direct productC4×#64750

Splittings

SylowC5 ⋊ C4×#343

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic5
commutatorC22×C5C43
FrattiniC23×C4C22×D5
FittingC2×C4×C5×C4⋊C4C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC23×C4×C5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C4×#343
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 74774);