Finite Group Databasebeta

C2×#13116998 #16017552

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

Aliases

direct productC2×#13116998

Splittings

SylowC13 ⋊ C2×#2229

Subgroups

subgroupG/H
centerC23D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#358C2
socle, prime radicalC23×C13C2×D8
hypercenterC2×#358D13
hypocenterC13C2×#2229
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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, 324201);