C₁₉×#33827 #18039786

order	4864
nilpotency class	4
isoclinism	isoclinic class of #33764
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#33827

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

464 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 194 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) = 91
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 91 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(28,29,34,39)(30,35,41,56)(31,44,47,78)(32,48,52,77)(33,53,50,38)(36,59,61,45)(37,62,64,51)(40,66,67,89)(42,72,70,88)(43,75,71,58)(46,79,54,63)(49,65,80,60)(55,81,82,68)(57,85,84,74)(69,90,76,86)(73,87,91,83);(20,21)(22,25)(23,24)(26,27)(28,30,34,41)(29,35,39,56)(31,40,47,67)(32,42,52,70)(33,43,50,71)(36,55,61,82)(37,57,64,84)(38,58,53,75)(44,66,78,89)(45,68,59,81)(46,69,54,76)(48,72,77,88)(49,73,80,91)(51,74,62,85)(60,83,65,87)(63,86,79,90);(21,24)(25,27)(28,31,34,47)(29,36,39,61)(30,40,41,67)(32,49,52,80)(33,54,50,46)(35,55,56,82)(37,63,64,79)(38,65,53,60)(42,73,70,91)(43,76,71,69)(44,77,78,48)(45,62,59,51)(57,86,84,90)(58,87,75,83)(66,88,89,72)(68,85,81,74);(20,22,23,26)(21,25,24,27)(30,41)(35,56)(40,67)(42,70)(43,71)(55,82)(57,84)(58,75)(66,89)(68,81)(69,76)(72,88)(73,91)(74,85)(83,87)(86,90)

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, 26815);