Finite Group Databasebeta

C2×#13131466 #16808112

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

Aliases

direct productC2×#13131466

Splittings

FittingC2×C13×H(5,𝔽2) ⋊ C4
SylowC13 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC22C22×C22⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC2×C13×H(5,𝔽2)C4
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719650C2
cosocleC4×D13C25
hypercenterC2×H(5,𝔽2)#261
hypocenterC13C2×#2901
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114761);