C₁₉×#12458 #18018417

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12430
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12458

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

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

normal subgroups only

This group has 192 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) = 4864

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

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5446);