Finite Group Databasebeta

D13×#2913 #16726587

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

Aliases

direct productD13×#2913

Splittings

FittingC13×#2913 ⋊ C2
SylowC13 ⋊ C2×#2913

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC13×#2913C2
socleC22×C13C23×D4
prime radicalC2×#41×D13C22
cosocleC2×C4×C13C25
hypercenter#2913D13
hypocenterC13C2×#2913
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2913

2766 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, 1033236);