C₁₉×#12464 #18018423

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12463
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12464

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1675
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 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)(20,21,27,33)(22,34,40,66)(23,41)(24,46,48,31)(25,30,35,61)(26,50,47,32)(28,51,55,37)(29,56)(36,69)(38,64,67,54)(39,53,74,65)(42,60)(43,77)(44,62)(45,57)(49,58)(52,71)(59,68)(63,78)(70,76)(72,80)(73,79)(75,82)(81,83);(20,22,35,67,26,39,24,37,27,40,25,38,47,74,48,51)(21,28,31,53,32,54,30,34,33,55,46,65,50,64,61,66)(23,36,68,83,43,71,42,70,45,73,49,75,44,72,56,78)(29,52,62,81,58,69,57,63,60,80,77,82,59,79,41,76);(20,23)(21,29)(22,36)(24,42)(25,49)(26,43)(27,45)(28,52)(30,57)(31,62)(32,58)(33,60)(34,63)(35,68)(37,70)(38,75)(39,71)(40,73)(41,61)(44,47)(46,77)(48,56)(50,59)(51,78)(53,81)(54,69)(55,80)(64,79)(65,82)(66,76)(67,83)(72,74)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5452);