Finite Group Databasebeta

C2×#13115566 #15866243

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13115566

Splittings

SylowC13 ⋊ C2×#1942

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#389C2
socle, prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC2×#389D13
hypocenterC13C2×#1942
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 172892);