Finite Group Databasebeta

C22×#11718860 #16730298

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11718860

Splittings

FittingC22×C13×AGL(1,ℤ/8) ⋊ C2
SylowC13 ⋊ C22×#472

Subgroups

subgroupG/H
centerC23#88193
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×AGL(1,ℤ/8)C2
socleC23×C13#121
hypercenterC22×AGL(1,ℤ/8)D13
hypocenterC13C22×#472
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036947);