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C16×C22⋊AGL(1,𝔽5) #13025727

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC16×C22⋊AGL(1,𝔽5)

Splittings

FittingC22×C5×C16 ⋊ C4
SylowC5 ⋊ C16×C22⋊C4

Subgroups

subgroupG/H
centerC2×C16C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C16
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC22×C5×C16C4
socleC22×C5C2×C4×C8
prime radicalC23×D5C2×C8
cosocleC2×C8×D5C23
hypercenterC22×C16AGL(1,𝔽5)
hypocenterC5C16×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C16 ◁ C22×C16

510 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, 1095995);