Finite Group Databasebeta

D13×#1764 #15860745

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD13×#1764

Splittings

FittingC13×#1764 ⋊ C2
SylowC13 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC2×C8D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1764C2
socleC22×C13C2×C4×D4
prime radicalC2×#41×D13C22
cosocleC22×C4×C13C24
hypercenter#1764D13
hypocenterC13C2×#1764
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1764

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167394);