Finite Group Databasebeta

C2×#13114567 #15860349

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13114567

Splittings

SylowC13 ⋊ C2×#1740

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC2×C13×#342C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenterC2×#342D13
hypocenterC13C2×#1740
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

2350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 166998);