Finite Group Databasebeta

#15768381

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #10772

Subgroups

subgroupG/H
centerC2×C4#88193
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#421C2
socleC22×C13#386
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenterC2×#421D13
hypocenterC13#10772
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

1298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Polycyclic presentation:

2^8,13|a^2=f,b^2=g,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^b=i^12,e^c=eh,f^c=fh

Conjugacy classes & character table

328 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 75030);