C₁₉×#8524 #18014483

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#8524

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

910 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1512);