C₁₉×#18732 #18024691

order	4864
nilpotency class	3
isoclinism	isoclinic class of #18712
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#18732

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

808 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(22,28)(23,30)(25,33)(26,31)(29,32)(34,35)(36,37,42,47)(38,48,51,61)(39,44,53,59)(40,46,41,45)(43,55,57,50)(49,62,65,66)(52,60,54,58)(56,63,67,64);(20,21,24,27)(22,25,29,34)(23,31,30,26)(28,35,32,33)(36,38)(37,43)(39,49)(40,50)(41,55)(42,51)(44,56)(45,48)(46,61)(47,57)(52,63)(53,65)(54,64)(58,66)(59,67)(60,62);(20,22)(21,25)(23,32)(24,29)(26,35)(27,34)(28,30)(31,33)(36,39,42,53)(37,44,47,59)(38,49,51,65)(40,54,41,52)(43,56,57,67)(45,60,46,58)(48,62,61,66)(50,64,55,63);(36,40,42,41)(37,45,47,46)(38,50,51,55)(39,52,53,54)(43,48,57,61)(44,58,59,60)(49,63,65,64)(56,66,67,62)

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, 11720);