Finite Group Databasebeta

#15919067

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #25852

Subgroups

subgroupG/H
centerC22C2×#88191
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC13×#2409C2
socleC22×C13C2×#120
prime radicalC22×D4×C13C23
hypercenter#2409D13
hypocenterC13#25852
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2409

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

2^8,13|a^2=e,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^12,c^b=cg,f^b=fh,g^c=gh,i^c=i^12

Conjugacy classes & character table

271 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 225716);