Finite Group Databasebeta

D13×#1937 #15865649

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

Aliases

direct productD13×#1937

Splittings

FittingC13×#1937 ⋊ C2
SylowC13 ⋊ C2×#1937

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1937C2
socleC22×C13C2×C4×D4
prime radicalC2×#41×D13C22
cosocleC22×C4×C13C24
hypercenter#1937D13
hypocenterC13C2×#1937
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

1114 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, 172298);