Finite Group Databasebeta

C2×#13112760 #15771978

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13112760

Splittings

SylowC13 ⋊ C2×#1314

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic13
commutatorC22×C13C22×C16
FrattiniC22×C8C22×D13
FittingC22×C13×C22⋊C8C2
socleC23×C13C22⋊C8
prime radicalC25×C13C8
cosocleC22×C8×C13C23
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#1314
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×C22⋊C8

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 78627);