C₁₉×#7528 #18013487

order	4864
nilpotency class	6
isoclinism	isoclinic class of #7527
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#7528

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1408
commutator	C₄×C₈	C₂×C₄×C₁₉
Frattini, cosocle	#492	C₂²×C₁₉
prime radical	C₁₉×#127	D₄
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#492 ◁ G

142 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 30 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 — 2 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)(22,31,33,44)(23,35,37,27)(24,29,40,28)(25,30)(26,32,41,49)(34,48,39,47)(36,43)(38,45,51,46)(42,50);(20,22,25,34)(21,26,30,41)(23,36,38,50)(24,39,40,33)(27,44,46,47)(28,43,29,42)(31,35,48,45)(32,37,49,51)

Conjugacy classes & character table

361 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 516);