Finite Group Databasebeta

C2×#13129917 #16789155

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13129917

Splittings

FittingC2×C13×M32 ⋊ C4
SylowC13 ⋊ C2×#1389

Subgroups

subgroupG/H
centerC22#11718265
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC2×C13×M32C4
socleC22×C13#340
prime radicalC23×D13SD16
cosocleC2×C8×D13C23
hypercenterC2×M32#261
hypocenterC13C2×#1389
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095804);