C₁₉×#9196 #18015155

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9183
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#9196

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

478 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 134 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)(20,21,25,26,24,22,23,27)(28,29)(30,38)(31,42,44,35)(32,45)(33,37)(34,40)(36,47)(39,52,55,59)(41,53)(43,50,46,51)(48,54,58,56)(49,57);(20,22,24,21)(23,27,25,26)(28,30,32,40,33,41,47,57)(29,34,36,38,37,49,45,53)(31,39,46,56,44,55,43,54)(35,48,51,52,42,58,50,59);(20,23,24,25)(21,26,22,27)(28,31)(29,35)(30,39)(32,46)(33,44)(34,48)(36,51)(37,42)(38,52)(40,56)(41,55)(43,47)(45,50)(49,58)(53,59)(54,57)

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, 2184);