Finite Group Databasebeta

C2×#13131130 #16806912

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

Aliases

direct productC2×#13131130

Splittings

SylowC13 ⋊ C2×#2132

Subgroups

subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#124C4
socleC22×C13C2×#99
prime radicalC2×#11719373C2
cosocleC2×Dic26C24
hypercenterC2×#124#261
hypocenterC13C2×#2132
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

1306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113561);