Finite Group Databasebeta

D13×#1658 #15844102

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD13×#1658

Splittings

FittingC13×#1658 ⋊ C2
SylowC13 ⋊ C2×#1658

Subgroups

subgroupG/H
centerC22D13×#120
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#1658C2
socleC22×C13C2×#120
prime radicalD13×#127C22
hypercenter#1658D13
hypocenterC13C2×#1658
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #1658

882 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 150751);