Finite Group Databasebeta

← Prev (#28399383) Next (#28399385) →

AGL(1,ℤ/8)×Dic113 #28399384

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

Aliases

direct productAGL(1,ℤ/8)×Dic113

Splittings

SylowC113 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting, prime radicalC2×AGL(1,ℤ/8)×C113C2
socleC22×C113C22×D4
cosocleC2×C4×C113C24
hypercenterC2×AGL(1,ℤ/8)D113
hypocenterC113C4×AGL(1,ℤ/8)
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13320);