Finite Group Databasebeta

Dic13×#578 #16727167

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productDic13×#578

Splittings

SylowC13 ⋊ C4×#578

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#578C2
socleC22×C13C23×D4
cosocleC2×C4×C13C25
hypercenterC2×#578D13
hypocenterC13C4×#578
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#578

2658 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, 1033816);