C₁₉×#13658 #18019617

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13657
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13658

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2177
commutator	C₁₆	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#2263	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₁₉×#346 ◁ G

194 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 82 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)(21,27,29,43)(22,32)(23,35)(24,39)(25,33)(28,36,40,44)(30,42,47,46)(31,48,41,45)(34,38)(37,49)(50,51);(20,21)(22,28)(23,36)(24,40)(25,41)(26,29)(27,34)(30,39)(31,33)(32,47)(35,43)(37,42)(38,44)(45,51)(46,50)(48,49);(20,22,33,39,26,24,25,32)(21,28,31,30,29,40,41,47)(23,35,50,49,38,34,37,51)(27,42,45,36,43,46,48,44)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6646);