Finite Group Databasebeta

#15770827

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #11207

Subgroups

subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#11207
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Polycyclic presentation:

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

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 77476);