Finite Group Databasebeta

← Prev (#16795208) Next (#16795210) →

AGL(1,ℤ/8)×#1057 #16795209

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#1057

Splittings

SylowC13 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
Fitting, prime radicalC2×C13×AGL(1,ℤ/8)C4
socleC22×C13C2×C4×D4
cosocleC4×Dic13C24
hypercenterC2×AGL(1,ℤ/8)#261
hypocenterC13C8×AGL(1,ℤ/8)
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1101858);