C₁₉×#12412 #18018371

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12412

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂×D₈×C₁₉	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#446 ◁ G

280 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 82 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)(20,21,26,30)(22,31,23,34)(24,29,25,28)(27,33,35,32)(36,37,42,46)(38,47,50,65)(39,44,41,56)(40,52,55,63)(43,58,60,49)(45,51,64,54)(48,66,57,62)(53,59,67,61);(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31)(36,38,42,50)(37,43,46,60)(39,48,41,57)(40,53,55,67)(44,59,56,61)(45,62,64,66)(47,63,65,52)(49,51,58,54);(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31)(36,39,42,41)(37,44,46,56)(38,48,50,57)(40,54,55,51)(43,59,60,61)(45,63,64,52)(47,62,65,66)(49,67,58,53)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5400);