Finite Group Databasebeta

D13×#2232 #16017673

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD13×#2232

Splittings

FittingC13×#2232 ⋊ C2
SylowC13 ⋊ C2×#2232

Subgroups

subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2232C2
socleC22×C13C22×D8
prime radicalD13×#466C2
hypercenter#2232D13
hypocenterC13C2×#2232
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 324322);