Finite Group Databasebeta

D13×#1772 #15860923

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productD13×#1772

Splittings

FittingC13×#1772 ⋊ C2
SylowC13 ⋊ C2×#1772

Subgroups

subgroupG/H
centerC2×C8D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1772C2
socleC22×C13C2×C4×D4
prime radicalC23×D13#41
cosocleC22×C4×C13C24
hypercenter#1772D13
hypocenterC13C2×#1772
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1772

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167572);