Finite Group Databasebeta

D13×#1458 #15828709

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productD13×#1458

Splittings

FittingC13×#1458 ⋊ C2
SylowC13 ⋊ C2×#1458

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC13×#1458C2
socleC22×C13C22×C22⋊C4
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1458D13
hypocenterC13C2×#1458
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

1390 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, 135358);