Finite Group Databasebeta

C2×#13123669 #16727017

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123669

Splittings

SylowC13 ⋊ C2×#2946

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
Fitting, prime radicalC22×C13×AGL(1,ℤ/8)C2
socleC23×C13C22×D4
cosocleC2×C4×C13C25
hypercenterC22×AGL(1,ℤ/8)D13
hypocenterC13C2×#2946
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033666);