Finite Group Databasebeta

D13×#2161 #16015972

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

Aliases

direct productD13×#2161

Splittings

FittingC13×#2161 ⋊ C2
SylowC13 ⋊ C2×#2161

Subgroups

subgroupG/H
centerC4C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2161C2
socleC2×C13C22×#107
prime radicalC23×D13Q16
cosocleC2×C8×C13C24
hypercenter#2161D13
hypocenterC13C2×#2161
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2161

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322621);