Finite Group Databasebeta

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C19×#2676 #14560533

order2432
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4

Aliases

direct productC19×#2676

Subgroups

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

676 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)(28,29,31,32)(30,33,34,35);(25,27)(29,32)(30,34);(20,21)(22,23)(24,25)(26,27)(28,29)(30,33)(31,32)(34,35);(20,21)(22,23)(28,30,31,34)(29,33,32,35)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#36706, C19×#36707, C19×#36712, …
maximal normal subgroup ofC19×#36706, C19×#36707, C19×#36712, …
maximal quotient ofC19×#14361, C19×#14362, C19×#14377, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1408);