Finite Group Databasebeta

#16016446

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #33479

Subgroups

subgroupG/H
centerC4×C8C22×D13
commutator, socleC22×C13C23×C8
FrattiniC2×C8C23×D13
FittingC8×C13×#41C2
prime radicalC2×C13×#41C8
cosocleC2×C8×C13C24
hypercenterC8×#41D13
hypocenterC13#33479
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C8×#41

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

2^8,13|a^2=f,c^2=f,d^2=e,f^2=g,g^2=h,b^a=be,c^a=ch,i^a=i^12,i^c=i^12

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323095);