Finite Group Databasebeta

#16837265

order3776
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC59 ⋊ #381

Subgroups

subgroupG/H
center, FrattiniC23C22×D59
commutatorC22×C59C22×C4
FittingC23×C4×C59C2
socle, cosocleC23×C59C23
prime radicalC24×C59C22
hypercenterC23×C4D59
hypocenterC59#381
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4

218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Polycyclic presentation:

2^6,59|a^2=f,c^2=d,b^a=bd,c^a=ce,g^a=g^58

Conjugacy classes & character table

956 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 412);