Finite Group Databasebeta

D13×#1401 #15783124

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD13×#1401

Splittings

FittingC13×#1401 ⋊ C2
SylowC13 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC16D4×D13
commutatorC4×C13C22×C16
FrattiniC2×C16C22×D13
FittingC13×#1401C2
socleC2×C13C2×C22⋊C16
prime radical#41×D13C8
cosocleC2×C13×C16C23
hypercenter#1401D13
hypocenterC13C2×#1401
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C16 ◁ C2×C16 ◁ #1401

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 89773);