C₁₉×#12399 #18018358

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#12399

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3341	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

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

normal subgroups only

This group has 290 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)(20,21,25,29)(22,30,33,34)(23,28,24,27)(26,32,35,31)(36,37,42,46)(38,47,50,66)(39,44,41,56)(40,52,55,64)(43,58,61,49)(45,51,63,54)(48,65,57,62)(53,59,67,60);(20,22,25,33)(21,26,29,35)(23,32,24,31)(27,34,28,30)(36,38,42,50)(37,43,46,61)(39,48,41,57)(40,53,55,67)(44,59,56,60)(45,62,63,65)(47,64,66,52)(49,51,58,54);(21,27)(23,24)(26,34)(28,29)(30,35)(31,32)(36,39,42,41)(37,44,46,56)(38,48,50,57)(40,51,55,54)(43,59,61,60)(45,52,63,64)(47,65,66,62)(49,53,58,67)

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, 5387);