Finite Group Databasebeta

Dic13×#349 #15777961

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic13×#349

Splittings

SylowC13 ⋊ C4×#349

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C2×C4×C8
FrattiniC22×C8C22×D13
FittingC2×C13×#349C2
socleC22×C13C2×C22⋊C8
prime radicalC24×C13C2×C8
cosocleC22×C8×C13C23
hypercenterC2×#349D13
hypocenterC13C4×#349
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

522 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, 84610);