C₁₉×#12290 #18018249

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12102
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12290

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#466	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊C₈ ◁ G

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 1216

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

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, 5278);