Finite Group Databasebeta

C19×#2161 #14560018

order2432
nilpotency class4
isoclinismisoclinic class of #509
automorphism?
homologyAbelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22

Aliases

direct productC19×#2161

Subgroups

subgroupG/H
centerC4×C19C2×D8
commutatorC8C22×C4×C19
Frattini, cosocleC2×C8C23×C19
socleC2×C19C2×#107
prime radicalC23×C19Q16
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C22×C8×C19 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,26,30,25,40)(22,31,35,47,33,45,36,50)(23,37,38,44,39,51,32,28)(27,41,43,49,42,48,46,34);(20,22,32,48,25,36,39,49,26,33,38,41,24,35,23,34)(21,27,37,47,29,43,44,45,30,42,51,50,40,46,28,31);(22,33)(27,42)(31,45)(34,49)(35,36)(41,48)(43,46)(47,50)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#12678, C19×#12924, C19×#12927, …
maximal normal subgroup ofC19×#12678, C19×#12924, C19×#12927, …
maximal quotient ofC19×#12009, C19×#12025, C19×#12032, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 893);