Finite Group Databasebeta

#15769411

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C27

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #10965

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC24×C13C22×C4
FrattiniC25C22×D13
Fitting, prime radicalC22×C13×#120C2
socleC23×C13C2×C22⋊C4
cosocleC25×C13C23
hypercenterC22×#120D13
hypocenterC13#10965
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C26 ◁ C22×#120

3098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Polycyclic presentation:

2^8,13|a^2=g,b^a=bd,c^a=ce,d^a=dh,i^a=i^12,c^b=cf,g^b=gh

Conjugacy classes & character table

388 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 76060);