C₁₉×#18731 #18024690

order	4864
nilpotency class	3
isoclinism	isoclinic class of #18712
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#18731

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

884 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 1216

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

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 11719);