Finite Group Databasebeta

← Prev (#14560527) Next (#14560529) →

C19×#2671 #14560528

order2432
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C25

Aliases

direct productC19×#2671

Subgroups

subgroupG/H
center, socleC23×C19C24
commutator, Frattini, cosocleC23C24×C19
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(28,29)(30,32)(31,33)(34,35);(25,27)(29,30)(31,35);(20,21)(22,23)(24,25)(26,27)(28,30,32,29)(31,34,35,33);(20,21)(22,23)(28,31)(29,33)(30,34)(32,35)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#36704, C19×#36706, C19×#36709, …
maximal normal subgroup ofC19×#36704, C19×#36706, C19×#36709, …
maximal quotient ofC19×#14359, C19×#14361, C19×#14363, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1403);