C₁₉×#2222 #14560079

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2221
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2222

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#466
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ G

140 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,27,33)(22,34,40,62)(23,41,44,58)(24,45,47,56)(25,32,26,31)(28,49,53,37)(29,48,55,43)(30,46,57,35)(36,65,68,82)(38,61,39,60)(42,73,74,54)(50,77,78,83)(51,69,52,63)(59,70,81,67)(64,72,75,80)(66,71,76,79);(20,22,35,63,26,39,47,49,27,40,46,69,25,38,24,37)(21,28,45,61,32,52,57,62,33,53,56,60,31,51,30,34)(23,36,64,83,43,67,74,76,44,68,75,77,48,70,42,66)(29,50,72,65,41,71,73,81,55,78,80,82,58,79,54,59);(20,23)(21,29)(22,36)(24,42)(25,48)(26,43)(27,44)(28,50)(30,54)(31,58)(32,41)(33,55)(34,59)(35,64)(37,66)(38,70)(39,67)(40,68)(45,72)(46,75)(47,74)(49,76)(51,79)(52,71)(53,78)(56,80)(57,73)(60,82)(61,65)(62,81)(63,83)(69,77)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13671, C₁₉×#13672, C₁₉×#13701, …
maximal normal subgroup of	C₁₉×#13671, C₁₉×#13672, C₁₉×#13701, …
maximal quotient of	C₁₉×#12431, C₁₉×#12434, C₁₉×#12440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 954);