Finite Group Databasebeta

C2×#13131372 #16807609

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×#13131372
unambiguous semidirect productD13⋊#2372

Splittings

FittingC2×C13×#124 ⋊ C4
SylowC13 ⋊ C2×#2372

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#124C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C22
cosocleC22×D13C25
hypercenterC2×#124#261
hypocenterC13C2×#2372
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

3158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1114258);