C₁₉×#32877 #18038836

order	4864
nilpotency class	3
isoclinism	isoclinic class of #32875
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#32877

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

594 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 186 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) = 608

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

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 25865);