Finite Group Databasebeta

← Prev (#31789598) Next (#31789600) →

AGL(1,ℤ/8)×Dic137 #31789599

order17536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×Dic137

Splittings

SylowC137 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D137
commutatorC4×C137C23×C4
FrattiniC2×C4C23×D137
Fitting, prime radicalC2×AGL(1,ℤ/8)×C137C2
socleC22×C137C22×D4
cosocleC2×C4×C137C24
hypercenterC2×AGL(1,ℤ/8)D137
hypocenterC137C4×AGL(1,ℤ/8)
LCSG ▷ C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4384

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 13320);