C₁₉×#16243 #18022202

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

Aliases

direct product

C₁₉×#16243

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

990 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 302 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)(22,26)(24,27)(28,29)(30,32)(31,34)(33,35)(36,37,39,40)(38,42,43,41)(44,45,48,47)(46,50,51,49);(29,30)(31,35)(37,40)(41,42)(44,46,48,51)(45,49,47,50);(20,21,23,25)(22,24,26,27)(28,30,32,29)(31,34,35,33)(36,38)(37,41)(39,43)(40,42)(44,46)(45,50)(47,49)(48,51);(20,22)(21,24)(23,26)(25,27)(28,31)(29,33)(30,34)(32,35)(36,37)(38,41)(39,40)(42,43)(44,47,48,45)(46,49,51,50)

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, 9231);