Finite Group Databasebeta

C2×#13126714 #16739316

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13126714

Splittings

FittingC2×C4×C13×Q16 ⋊ C2
SylowC13 ⋊ C2×#3299

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C4×C13×Q16C2
socleC23×C13C22×D4
prime radicalC22×D52D4
hypercenterC2×C4×Q16D13
hypocenterC13C2×#3299
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1045965);