C₁₉×#16248 #18022207

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₉×#16248

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

1250 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 350 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)(28,29)(30,32)(31,33)(34,35)(36,37,39,40)(38,41,42,43)(47,51)(49,50);(21,24)(25,27)(29,30)(31,35)(37,40)(38,42)(44,45,48,46)(47,49,51,50);(20,21,23,24)(22,25,26,27)(28,30,32,29)(31,34,35,33)(36,38)(37,41)(39,42)(40,43)(44,46,48,45)(47,50,51,49);(20,22,23,26)(21,25,24,27)(28,31,32,35)(29,33,30,34)(36,37)(38,41)(39,40)(42,43)(44,47)(45,49)(46,50)(48,51)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 9236);