Finite Group Databasebeta

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C22×D5⋊(C22⋊C8) #13044412

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC22×D5⋊(C22⋊C8)
unambiguous semidirect productD5⋊(C22×C22⋊C8)

Splittings

SylowC5 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×AGL(1,𝔽5)
commutatorC2×C5C24×C8
FrattiniC22C24×AGL(1,𝔽5)
FittingC24×C4×C5C4
socleC24×C5C22×C4
prime radicalC25×D5C4
cosocleC2×Dic5C25
hypercenterC24×C4AGL(1,𝔽5)
hypocenterC5C23×C22⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C24×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114680);