C₁₉×#18551 #18024510

order	4864
nilpotency class	3
isoclinism	isoclinic class of #18524
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#18551

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

918 conjugacy classes of subgroups; only the 246 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 246 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) = 2432

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

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, 11539);