C₁₉×#12409 #18018368

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12409

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

270 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 67
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,30)(22,31,23,34)(24,29,25,28)(27,33,35,32)(36,37,42,46)(38,47,50,65)(39,44,41,56)(40,52,55,66)(43,58,61,49)(45,51,63,54)(48,64,57,62)(53,59,67,60);(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31)(36,38)(37,43)(39,48)(40,53)(41,57)(42,50)(44,59)(45,62)(46,61)(47,52)(49,54)(51,58)(55,67)(56,60)(63,64)(65,66);(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31)(36,39,42,41)(37,44,46,56)(38,48,50,57)(40,51,55,54)(43,59,61,60)(45,52,63,66)(47,64,65,62)(49,53,58,67)

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, 5397);