Finite Group Databasebeta

#14561832

order2432
automorphism?
homologyAbelianization (H1) = C2×C16 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC19 ⋊ #1422

Subgroups

subgroupG/H
centerC16C22⋊D19
commutatorC4×C19C2×C16
FrattiniC2×C16C2×D19
FittingC19×M64C2
socleC2×C19C4⋊C16
prime radicalC22×C19M32
cosocleC2×C16×C19C22
hypercenterM64D19
hypocenterC19#1422
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C16 ◁ C2×C16 ◁ M64

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Polycyclic presentation:

2^7,19|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^b=h^18

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

maximal quotient of#18070204, #18070211, #18070229

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2707);