C₁₉×#12388 #18018347

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12388

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3403	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#446 ◁ G

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

normal subgroups only

This group has 296 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) = 2432

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

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, 5376);