Finite Group Databasebeta

← Prev (#16828301) Next (#16828303) →

AGL(1,ℤ/8)×Dic29 #16828302

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×Dic29

Splittings

SylowC29 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
Fitting, prime radicalC2×C29×AGL(1,ℤ/8)C2
socleC22×C29C22×D4
cosocleC2×C4×C29C24
hypercenterC2×AGL(1,ℤ/8)D29
hypocenterC29C4×AGL(1,ℤ/8)
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

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(3712, 13320);