Finite Group Databasebeta

C2×#13115305 #15864745

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115305

Splittings

SylowC13 ⋊ C2×#1901

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊Q8C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#1901
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

1854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171394);