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AGL(1,ℤ/8)×#89137 #28379787

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#89137

Splittings

FittingAGL(1,ℤ/8)×C109 ⋊ C4
SylowC109 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingAGL(1,ℤ/8)×C109C4
socleC2×C109C2×C4×D4
prime radicalAGL(1,ℤ/8)×D109C2
cosocleC4×D109C24
hypercenterAGL(1,ℤ/8)#89137
hypocenterC109C4×AGL(1,ℤ/8)
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 872

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21265);