Finite Group Databasebeta

#15754184

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

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #8288

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socle, prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8288
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Polycyclic presentation:

2^8,13|a^2=e,b^2=f,c^2=de,d^2=g,e^2=h,b^a=bd,c^a=ch,d^b=dg,e^b=eg,i^b=i^12,i^c=i^12

Conjugacy classes & character table

412 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 60833);