Finite Group Databasebeta

Dic13×#359 #15778145

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic13×#359

Splittings

SylowC13 ⋊ C4×#359

Subgroups

subgroupG/H
centerC2×C4D8×D13
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#359C2
socleC22×C13C2×#102
prime radicalC2×C13×#135C22
cosocleC22×C8×C13C23
hypercenterC2×#359D13
hypocenterC13C4×#359
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

450 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, 84794);