C₁₉×#12398 #18018357

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12398

Subgroups

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

286 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,21,25,29)(22,30,33,34)(23,28,24,27)(26,32,35,31)(36,37,41,45)(38,46,49,65)(39,50,54,64)(40,55,52,44)(42,57,59,47)(43,60,62,53)(48,66,56,61)(51,63,67,58);(20,22,25,33)(21,26,29,35)(23,32,24,31)(27,34,28,30)(36,38,41,49)(37,42,45,59)(39,51,54,67)(40,56,52,48)(43,61,62,66)(44,63,55,58)(46,64,65,50)(47,60,57,53);(21,27)(23,24)(26,34)(28,29)(30,35)(31,32)

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, 5386);