C₁₉×#23840 #18029799

order	4864
nilpotency class	3
isoclinism	isoclinic class of #23391
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#23840

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 4864

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16828);