C₁₉×#8753 #18014712

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#8753

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

566 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 118 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)(22,26,27,24)(23,25)(28,29,32,37,33,36,46,51)(30,38,40,52,41,34,45,48)(31,42,44,56,43,35,49,50)(39,47,55,58,54,53,57,59);(28,30,33,41)(29,34,36,38)(31,39,43,54)(32,45,46,40)(35,47,42,53)(37,52,51,48)(44,57,49,55)(50,59,56,58);(20,22)(21,24)(23,27)(25,26)(28,31)(29,35,36,42)(30,39)(32,44)(33,43)(34,47,38,53)(37,50,51,56)(40,55)(41,54)(45,57)(46,49)(48,58,52,59)

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, 1741);