Finite Group Databasebeta

Dic13×#343 #15768123

order3328
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productDic13×#343

Splittings

SylowC13 ⋊ C4×#343

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C43
FrattiniC23×C4C22×D13
FittingC2×C13×#343C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×C4×C13C23
hypercenterC2×#343D13
hypocenterC13C4×#343
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 74772);