Finite Group Databasebeta

#15753963

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #8248

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊Dic13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#2966C2
socleC22×C13C4×C22⋊C4
prime radicalC13×#121C2×C4
cosocleC2×C42×C13C23
hypercenter#2966D13
hypocenterC13#8248
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

2^8,13|a^2=e,b^2=f,c^2=e,d^2=g,e^2=h,b^a=bd,d^a=dg,f^a=fgh,c^b=cg,d^b=dh,i^b=i^12

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, 60612);