Finite Group Databasebeta

D13×#2070 #15891638

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

Aliases

direct productD13×#2070

Splittings

FittingC13×#2070 ⋊ C2
SylowC13 ⋊ C2×#2070

Subgroups

subgroupG/H
centerC2D13×#396
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2070C2
socleC2×C13C2×#396
prime radicalC23×D13C2×Q8
hypercenter#2070D13
hypocenterC13C2×#2070
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2070

950 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 207 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) = 416

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 198287);