Finite Group Databasebeta

D13×#2153 #16015916

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

Aliases

direct productD13×#2153

Splittings

FittingC13×#2153 ⋊ C2
SylowC13 ⋊ C2×#2153

Subgroups

subgroupG/H
centerC8C2×D4×D13
commutatorC4×C13C23×C8
FrattiniC2×C8C23×D13
FittingC13×#2153C2
socleC2×C13C22×C4⋊C8
prime radicalC23×D13M16
cosocleC2×C8×C13C24
hypercenter#2153D13
hypocenterC13C2×#2153
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2153

698 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, 322565);