C₁₉×#2214 #14560071

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2214

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 150 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) = 51
transitive degree	μ_t(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)(20,21,27,33)(22,31,36,42)(23,37,39,50)(24,32,26,30)(25,28,35,43)(29,44,46,34)(38,51,41,47)(40,48,49,45);(20,22,26,35,27,36,24,25)(21,28,32,42,33,43,30,31)(23,34,41,49,39,44,38,40)(29,37,48,51,46,50,45,47);(20,23)(21,29)(22,34)(24,38)(25,40)(26,41)(27,39)(28,37)(30,45)(31,47)(32,48)(33,46)(35,49)(36,44)(42,51)(43,50)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12312, C₁₉×#12313, C₁₉×#12315, …
maximal normal subgroup of	C₁₉×#12312, C₁₉×#12313, C₁₉×#12315, …
maximal quotient of	C₁₉×#12422, C₁₉×#12423, C₁₉×#12426, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 946);