Finite Group Databasebeta

D13×#1515 #15830181

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD13×#1515

Splittings

FittingC13×#1515 ⋊ C2
SylowC13 ⋊ C2×#1515

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1515C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1515D13
hypocenterC13C2×#1515
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 136830);