Finite Group Databasebeta

#15770790

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #11199

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC22×C13×C22⋊C8C2
socleC24×C13C2×D4
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC22×C22⋊C8D13
hypocenterC13#11199
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

2^8,13|a^2=g,c^2=d,e^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^12,c^b=cf,e^c=eh,i^c=i^12

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 77439);