Finite Group Databasebeta

#15769407

order3328
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C27

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #10964

Subgroups

subgroupG/H
center, FrattiniC23×C4C22×D13
commutatorC23×C13C22×C8
FittingC22×C4×D4×C13C2
socleC24×C13C22×C4
prime radicalC23×D4×C13C4
cosocleC23×C4×C13C23
hypercenterC22×C4×D4D13
hypocenterC13#10964
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

1902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

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

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 76056);