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AGL(1,ℤ/8)×#90673 #28407329

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#90673

Splittings

FittingAGL(1,ℤ/8)×C113 ⋊ C4
SylowC113 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
FittingAGL(1,ℤ/8)×C113C4
socleC2×C113C2×C4×D4
prime radicalAGL(1,ℤ/8)×D113C2
cosocleC4×D113C24
hypercenterAGL(1,ℤ/8)#90673
hypocenterC113C4×AGL(1,ℤ/8)
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21265);