Finite Group Databasebeta

C2×#13131246 #16807227

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13131246

Splittings

FittingC2×C13×D16 ⋊ C4
SylowC13 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#11719102
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×D16C4
socleC22×C13#442
prime radicalC2×#11718572C2
cosocleC8×D13C24
hypercenterC2×D16#261
hypocenterC13C2×AGL(1,ℤ/16)
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113876);