C₁₉×#8797 #18014756

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8790
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#8797

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#382
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 228 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)(20,21,24,29,25,30,32,28)(22,31,23,26,33,27,34,35)(36,37,40,45,41,44,47,56)(38,46,50,58,51,42,49,59)(39,52,54,43,55,61,53,60)(48,63,64,57,65,67,66,62);(20,22,32,34,25,33,24,23)(21,26,29,27,30,35,28,31)(36,38,47,50,41,51,40,49)(37,42,56,59,44,46,45,58)(39,48,54,66,55,65,53,64)(43,57,61,63,60,62,52,67);(20,23,24,33,25,34,32,22)(21,27,28,26,30,31,29,35)(36,39)(37,43,44,60)(38,48)(40,53)(41,55)(42,57,46,62)(45,52,56,61)(47,54)(49,64)(50,66)(51,65)(58,67,59,63)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1785);