Finite Group Databasebeta

#15785142

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

No aliases for this group.

Splittings

FittingC13×#1437 ⋊ C2
SylowC13 ⋊ #13903

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×D13C22
hypercenter#1437D13
hypocenterC13#13903
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

3526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

2^8,13|a^2=h,b^2=eg,b^a=be,c^a=cf,d^a=de,c^b=cg,i^b=i^12,i^d=i^12

Conjugacy classes & character table

412 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91791);