C₁₉×#8758 #18014717

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#8758

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

394 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 110 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 — 3 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)(22,28,30,25)(23,31)(24,27)(26,32)(29,33,35,34)(36,37,39,43,40,42,46,49)(38,41,44,48,45,47,50,51);(20,22)(21,25)(23,29)(24,30)(26,33)(27,28)(31,34)(32,35)(36,38,40,45)(37,41,42,47)(39,44,46,50)(43,48,49,51);(20,23)(21,26,27,31)(22,29)(24,32)(25,33,28,34)(30,35)(37,42)(39,46)(41,47)(44,50)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1746);