C₁₉×#11863 #18017822

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11855
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11863

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

304 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 3 generators on 67 points:

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

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, 4851);