Finite Group Databasebeta

C2×#13126791 #16739423

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13126791

Splittings

FittingC2×C13×#547 ⋊ C2
SylowC13 ⋊ C2×#3306

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13C2×#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

2514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1046072);