C₁₉×#23795 #18029754

order	4864
nilpotency class	3
isoclinism	isoclinic class of #23414
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#23795

Subgroups

	subgroup	G/H
center	C₄×C₁₉	C₂×#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	#2397
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

908 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 250 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 — 4 generators on 51 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16783);