C₁₉×#11970 #18017929

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11970

Subgroups

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

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

normal subgroups only

This group has 284 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)(20,21,23,27,24,26,32,34)(22,28,29,35,30,25,31,33)(36,37,41,47,42,45,57,63,43,48,55,65,39,54,40,46)(38,49,52,62,50,64,51,59,53,66,56,44,58,60,67,61);(20,22,24,30)(21,25,26,28)(23,31,32,29)(27,35,34,33)(36,38)(37,44)(39,50)(40,56)(41,51)(42,58)(43,53)(45,59)(46,64)(47,49)(48,62)(52,57)(54,61)(55,67)(60,63)(65,66);(21,26)(25,28)(27,34)(33,35)(36,39,43,42)(37,45,48,54)(38,50,53,58)(40,55,57,41)(44,59,62,61)(46,47,63,65)(49,60,66,64)(51,56,67,52)

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, 4958);