Finite Group Databasebeta

D13×#2123 #16015653

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD13×#2123

Splittings

FittingC13×#2123 ⋊ C2
SylowC13 ⋊ C2×#2123

Subgroups

subgroupG/H
centerC2C2×D13×#99
commutatorC23×C13C23×C4
FrattiniC2×D4C23×D13
FittingC13×#2123C2
socleC2×C13C22×#99
prime radicalC2×#41×D13C22
cosocleC2×D4×C13C24
hypercenter#2123D13
hypocenterC13C2×#2123
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322302);