Finite Group Databasebeta

D13×#1757 #15860615

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

Aliases

direct productD13×#1757

Splittings

FittingC13×#1757 ⋊ C2
SylowC13 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC8C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1757C2
socleC2×C13C2×C4×C22⋊C4
prime radicalC2×#41×D13C22
cosocleC22×C4×C13C24
hypercenter#1757D13
hypocenterC13C2×#1757
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1757

1474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 167264);