C₁₉×#12502 #18018461

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12502

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

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

normal subgroups only

This group has 200 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) = 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)(20,21,24,27)(22,28,30,35)(23,32,29,26)(25,33,34,31)(36,37)(38,46)(39,42)(40,52)(41,55)(43,48)(44,54)(45,51)(47,62)(49,66)(50,63)(53,61)(56,60)(57,64)(58,65)(59,67);(20,22,29,33,24,30,23,31)(21,25,32,35,27,34,26,28)(37,42)(43,57)(44,58)(45,55)(46,62)(52,63)(59,61)(60,66);(22,30)(25,34)(28,35)(31,33)(36,38,39,47)(37,43,42,57)(40,53,50,67)(41,56,51,49)(44,60,58,66)(45,61,55,59)(46,63,62,52)(48,65,64,54)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5490);