C₁₉×#10586 #18016545

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10586

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

350 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 4864

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)(20,21,24,26)(22,27,23,25)(28,29,33,37)(30,34,40,43)(31,35,32,36)(38,41,39,42)(44,45)(46,53)(47,51)(48,50)(49,54)(52,56)(55,59)(57,58);(20,22,24,23)(21,25,26,27)(28,30)(29,34)(31,39)(32,38)(33,40)(35,42)(36,41)(37,43)(44,46,47,54)(45,49,51,53)(48,57,56,55)(50,59,52,58);(20,23,24,22)(21,25,26,27)(29,35)(30,38)(31,32)(36,37)(39,40)(41,42)(45,50)(48,56)(49,58)(51,52)(53,59)(55,57)

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, 3574);