C₁₉×#8540 #18014499

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8534
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#8540

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#534	C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

718 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 142 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)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33)(36,37,40,44,41,45,51,57)(38,42,48,54,47,53,61,65)(39,43,50,56,49,55,62,66)(46,58,60,67,59,52,63,64);(20,22)(21,25)(23,29)(24,30)(26,32)(27,28)(31,35)(33,34)(36,38)(37,42)(39,46)(40,48)(41,47)(43,52)(44,54)(45,53)(49,59)(50,60)(51,61)(55,58)(56,64)(57,65)(62,63)(66,67);(20,23,24,31)(21,26,27,33)(22,29,30,35)(25,32,28,34)(36,39)(37,43)(38,46)(40,50)(41,49)(42,52)(44,56)(45,55)(47,59)(48,60)(51,62)(53,58)(54,64)(57,66)(61,63)(65,67)

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, 1528);