Finite Group Databasebeta

#14565393

order2432
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC19 ⋊ #2151

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×D19
commutator, socleC22×C19C22×C8
FittingC22×C16×C19C2
prime radicalC23×C19C2×C8
cosocleC2×C8×C19C23
hypercenterC22×C16D19
hypocenterC19#2151
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C8 ◁ C22×C16

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Polycyclic presentation:

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

Conjugacy classes & character table

632 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#18069939
maximal normal subgroup of#18069939

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6268);