Finite Group Databasebeta

C2×#13113163 #15828756

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13113163

Splittings

SylowC13 ⋊ C2×#1462

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC23×C13×C22⋊C4C2
socleC23×C13C2×C22⋊C4
prime radicalC26×C13C4
cosocleC22×C4×C13C24
hypercenterC23×C22⋊C4D13
hypocenterC13C2×#1462
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C22⋊C4

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135405);