Finite Group Databasebeta

C2×#13117099 #16018328

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13117099

Splittings

FittingC22×C13×D16 ⋊ C2
SylowC13 ⋊ C2×#2250

Subgroups

subgroupG/H
centerC23D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC22×C13×D16C2
socleC23×C13C2×D8
hypercenterC22×D16D13
hypocenterC13C2×#2250
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 324977);