C₁₉×#11539 #18017498

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11521
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11539

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#1467
prime radical	C₂³×C₁₉	C₂×M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₁₉×#405 ◁ G

270 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,25,29,40,46,26,31,38,48,23,27,37,42)(22,32,34,49,35,45,50,47,36,41,39,51,33,28,43,44);(21,27,31,29)(24,38)(28,41,45,32)(30,42,48,46)(34,39)(37,40)(43,50)(44,51,47,49);(20,22,25,35,26,36,23,33)(21,28,27,41,31,45,29,32)(24,39,40,43,38,34,37,50)(30,47,42,49,48,44,46,51)

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, 4527);