Finite Group Databasebeta

D13×#1300 #15753109

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productD13×#1300

Splittings

FittingC13×#1300 ⋊ C2
SylowC13 ⋊ C2×#1300

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1300C2
socleC22×C13C2×#95
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1300D13
hypocenterC13C2×#1300
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 59758);