Finite Group Databasebeta

D13×#2158 #16015944

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD13×#2158

Splittings

FittingC13×#2158 ⋊ C2
SylowC13 ⋊ C2×#2158

Subgroups

subgroupG/H
centerC2×C4D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2158C2
socleC22×C13C22×D8
prime radicalC23×D13D8
cosocleC2×C8×C13C24
hypercenter#2158D13
hypocenterC13C2×#2158
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 322593);