Finite Group Databasebeta

#14572579

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC19 ⋊ #2962

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D19
commutator, socleC22×C19C23×C4
FittingC19×#405C2
prime radicalC23×C19C22×C4
cosocleC2×C4×C19C24
hypercenter#405D19
hypocenterC19#2962
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ #405

356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Polycyclic presentation:

2^7,19|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,h^b=h^18,d^c=dg

Conjugacy classes & character table

410 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 13454);