Finite Group Databasebeta

C2×#13123381 #16726516

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13123381

Splittings

FittingC2×C13×#568 ⋊ C2
SylowC13 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#568C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719648C2
cosocleC2×C4×C13C25
hypercenterC2×#568D13
hypocenterC13C2×#2901
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×#41 ◁ C2×#568

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033165);