C₁₉×#23794 #18029753

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

Aliases

direct product

C₁₉×#23794

Subgroups

	subgroup	G/H
center	C₈×C₁₉	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	#2397
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

930 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 250 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)(20,21,24,28,25,29,37,43)(22,30,32,38,33,42,36,26)(23,27,34,40,35,41,48,51)(31,44,45,49,46,50,47,39);(20,22)(21,26)(23,31)(24,36)(25,33)(27,39)(28,42)(29,38)(30,43)(32,37)(34,47)(35,46)(40,50)(41,49)(44,51)(45,48);(26,38)(30,42)(39,49)(44,50);(20,23,24,34,25,35,37,48)(21,27,28,40,29,41,43,51)(22,31,36,47,33,46,32,45)(26,39,42,50,38,49,30,44)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16782);