Finite Group Databasebeta

D13×#2117 #16015618

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD13×#2117

Splittings

FittingC13×#2117 ⋊ C2
SylowC13 ⋊ C2×#2117

Subgroups

subgroupG/H
centerC8C2×D4×D13
commutatorC4×C13C23×C8
FrattiniC2×C8C23×D13
FittingC13×#2117C2
socleC2×C13C22×C22⋊C8
prime radicalC2×#41×D13C4
cosocleC2×C8×C13C24
hypercenter#2117D13
hypocenterC13C2×#2117
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

1154 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, 322267);