Finite Group Databasebeta

C2×#13124241 #16729657

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

Aliases

direct productC2×#13124241

Splittings

FittingC2×C13×#536 ⋊ C2
SylowC13 ⋊ C2×#3028

Subgroups

subgroupG/H
centerC22C2×#88191
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#536C2
socleC22×C13C2×#120
prime radicalC2×#11719648C2
hypercenterC2×#536D13
hypocenterC13C2×#3028
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

4790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036306);