C₁₉×#11869 #18017828

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11867
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#11869

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1519
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 83 points:

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

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, 4857);