Finite Group Databasebeta

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C4×#65248 #12021093

order1280
isoclinismisoclinic class of #64945
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC4×#65248

Splittings

FittingC2×C4×C5×C22⋊C4 ⋊ C2
SylowC5 ⋊ C4×#394

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×C4×C22⋊C4D5
hypocenterC5C4×#394
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

2550 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, 91361);