C₁₉×#32764 #18038723

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₁₉×#32764

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

936 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 51
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 51 points:

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

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, 25752);