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C2×AGL(1,ℤ/8)×D251 #44565095

order32128
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,ℤ/8)×D251

Splittings

FittingC2×AGL(1,ℤ/8)×C251 ⋊ C2
SylowC251 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D251
commutator, cosocleC4×C251C25
FrattiniC4C24×D251
FittingC2×AGL(1,ℤ/8)×C251C2
socleC22×C251C22×D4
hypercenterC2×AGL(1,ℤ/8)D251
hypocenterC251C22×AGL(1,ℤ/8)
LCSG ▷ C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4016

Conjugacy classes & character table

2794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 19240);