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C22×(C2×AGL(1,𝔽5))⋊C8 #13033123

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×(C2×AGL(1,𝔽5))⋊C8

Splittings

FittingC23×C5×C8 ⋊ C4
SylowC5 ⋊ C22×#336

Subgroups

subgroupG/H
centerC23×C4C2×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC24×C5C42
prime radicalC24×D5C2×C4
cosocleC2×C4×D5C24
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5C22×#336
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C23×C8

3086 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, 1103391);