C₁₉×#12284 #18018243

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12284

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3199	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 1216

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

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5272);