Finite Group Databasebeta

C2×#13117032 #16017681

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

Aliases

direct productC2×#13117032

Splittings

FittingC2×C13×#358 ⋊ C2
SylowC13 ⋊ C2×#2235

Subgroups

subgroupG/H
centerC23D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#358C2
socleC23×C13C2×D8
prime radicalC23×D13D8
hypercenterC2×#358D13
hypocenterC13C2×#2235
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

630 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, 324330);