C₁₉×#32876 #18038835

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

Aliases

direct product

C₁₉×#32876

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 584 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)(20,21,25,29)(22,30,32,26)(23,34,36,27)(24,38,40,28)(31,46,47,41)(33,42,39,45)(35,43,50,48)(37,44,51,49);(20,22,24,39,25,32,40,33)(21,26,28,45,29,30,38,42)(23,35,37,31,36,50,51,47)(27,43,44,41,34,48,49,46);(20,23,24,37,25,36,40,51)(21,27,28,44,29,34,38,49)(22,31,33,35,32,47,39,50)(26,41,42,43,30,46,45,48);(31,47)(35,50)(41,46)(43,48)

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, 25864);