Finite Group Databasebeta

#16727563

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #60215

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
Fitting, prime radicalC13×#3475C2
cosocleC2×C4×C13C25
hypercenter#3475D13
hypocenterC13#60215
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #3475

1970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

2^8,13|a^2=g,c^2=g,d^2=f,g^2=h,b^a=bf,i^a=i^12,i^c=i^12,e^d=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, 1034212);