Finite Group Databasebeta

C2×#13124227 #16729640

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

Aliases

direct productC2×#13124227

Splittings

FittingC2×C13×#525 ⋊ C2
SylowC13 ⋊ C2×#3025

Subgroups

subgroupG/H
centerC2×C4#88191
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#525C2
socleC22×C13C2×#120
hypercenterC2×#525D13
hypocenterC13C2×#3025
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#525

5086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036289);