Finite Group Databasebeta

D13×#2178 #16016315

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

Aliases

direct productD13×#2178

Splittings

FittingC13×#2178 ⋊ C2
SylowC13 ⋊ C2×#2178

Subgroups

subgroupG/H
centerC8D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2178C2
socleC2×C13C2×C4×D8
prime radicalD13×#508C2
cosocleC2×C8×C13C24
hypercenter#2178D13
hypocenterC13C2×#2178
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ #2178

662 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, 322964);