C₁₉×#12840 #18018799

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12026
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12840

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#427
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1808
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

354 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 154 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)(20,21,25,32,27,31,26,48)(22,33,37,60,39,59,38,69)(23,40,42,55,43,29,47,54)(24,44,45,56,46,75,34,30)(28,49,52,67,51,61,58,36)(35,63,65,81,66,57,68,80)(41,72,62,71,73,74,76,53)(50,77,78,64,70,82,79,83);(20,22,34,61,26,38,46,67,27,39,45,49,25,37,24,36)(21,28,44,60,32,52,56,59,31,51,75,69,48,58,30,33)(23,35,62,82,42,65,73,83,43,66,76,77,47,68,41,64)(29,50,74,81,55,79,71,63,40,70,72,80,54,78,53,57);(20,23)(21,29)(22,35)(24,41)(25,47)(26,42)(27,43)(28,50)(30,53)(31,40)(32,55)(33,57)(34,62)(36,64)(37,68)(38,65)(39,66)(44,74)(45,76)(46,73)(48,54)(49,77)(51,70)(52,79)(56,71)(58,78)(59,63)(60,81)(61,82)(67,83)(69,80)(72,75)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5828);