Finite Group Databasebeta

#16837178

order3776
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC59 ⋊ #346

Subgroups

subgroupG/H
center, FrattiniC2×C8C2×D59
commutatorC2×C59C4×C8
FittingC4×C8×C59C2
socle, prime radicalC22×C59C2×C8
cosocleC2×C8×C59C22
hypercenterC4×C8D59
hypocenterC59#346
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C4×C8

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Polycyclic presentation:

2^6,59|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^58

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 325);