Finite Group Databasebeta

C2×#13131435 #16808067

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

Aliases

direct productC2×#13131435

Splittings

FittingC23×D4×C13 ⋊ C4
SylowC13 ⋊ C2×#2883

Subgroups

subgroupG/H
centerC22C22×C22⋊#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC23×D4×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC22×#88251C2
cosocleC22×D13C25
hypercenterC23×D4#261
hypocenterC13C2×#2883
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×D4 ◁ C23×D4

5338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

202 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114716);