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C8×(C2×AGL(1,𝔽5))⋊C4 #13021563

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×(C2×AGL(1,𝔽5))⋊C4

Splittings

FittingC2×C4×C5×C8 ⋊ C4
SylowC5 ⋊ C8×#95

Subgroups

subgroupG/H
centerC22×C8C2×AGL(1,𝔽5)
commutatorC2×C5C42×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC23×C5C2×C42
prime radicalC23×D5C22×C4
cosocleC22×C4×D5C23
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C8×#95
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1174 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, 1091831);