Finite Group Databasebeta

C2×#13123252 #16726315

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#13123252

Splittings

FittingC2×C13×#405 ⋊ C2
SylowC13 ⋊ C2×#2873

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC2×C13×#405C2
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC2×C4×C13C25
hypercenterC2×#405D13
hypocenterC13C2×#2873
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#405

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1032964);