C₁₉×#7086 #18013045

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7076
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7086

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#327
commutator	C₂²×C₈	C₂×C₄×C₁₉
Frattini, cosocle	C₂×C₂²⋊C₈	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	SD₁₆
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₂²⋊C₈ ◁ G

264 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 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)(22,26,27,24)(23,25)(28,29,32,37,34,38,33,49)(30,39,41,53,43,56,42,59)(31,44,46,36,48,54,47,55)(35,45,50,58,52,57,51,40);(21,24)(25,26)(28,30,34,43)(29,35,38,52)(31,45,48,57)(32,42,33,41)(36,53,55,59)(37,50,49,51)(39,54,56,44)(40,47,58,46)

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, 74);