Finite Group Databasebeta

C2×#13124233 #16729647

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13124233

Splittings

FittingC22×C13×H(5,𝔽2) ⋊ C2
SylowC13 ⋊ C2×#3026

Subgroups

subgroupG/H
centerC22C2×#88207
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×H(5,𝔽2)C2
socleC22×C13C2×#120
hypercenterC22×H(5,𝔽2)D13
hypocenterC13C2×#3026
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ C22×H(5,𝔽2)

5318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036296);