Finite Group Databasebeta

C2×#13123294 #16726386

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

Aliases

direct productC2×#13123294

Splittings

FittingC22×C13×#99 ⋊ C2
SylowC13 ⋊ C2×#2883

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C13×#99C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#88251C2
cosocleC23×C13C25
hypercenterC22×#99D13
hypocenterC13C2×#2883
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

5338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033035);