Finite Group Databasebeta

C2×#13117018 #16017678

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13117018

Splittings

FittingC2×C13×#366 ⋊ C2
SylowC13 ⋊ C2×#2232

Subgroups

subgroupG/H
centerC23D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#366C2
socleC23×C13C2×D8
prime radicalC2×#11718544C2
hypercenterC2×#366D13
hypocenterC13C2×#2232
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 324327);