Finite Group Databasebeta

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C4×#64705 #11990241

order1280
isoclinismisoclinic class of #64671
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#64705

Splittings

FittingC4×C5×C4⋊C8 ⋊ C2
SylowC5 ⋊ C4×#331

Subgroups

subgroupG/H
centerC22×C4#685
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC4×C5×C4⋊C8C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenterC4×C4⋊C8D5
hypocenterC5C4×#331
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 60509);