Finite Group Databasebeta

C2×#13123315 #16726414

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13123315

Splittings

SylowC13 ⋊ C2×#2888

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
Fitting, prime radicalC22×C13×H(5,𝔽2)C2
socleC22×C13C22×C22⋊C4
cosocleC2×C4×C13C25
hypercenterC22×H(5,𝔽2)D13
hypocenterC13C2×#2888
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×H(5,𝔽2)

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033063);