Finite Group Databasebeta

C2×#13118642 #16030400

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13118642

Splittings

FittingC22×C13×C22⋊Q8 ⋊ C2
SylowC13 ⋊ C2×#2449

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2449
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

3830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 337049);