C₁₉×#13333 #18019292

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13333

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

546 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,37)(27,43)(28,46)(29,35)(30,49)(31,36)(32,39)(33,42)(34,38)(40,52)(41,51)(44,50)(45,54)(47,53)(48,55);(21,23)(24,26,31,42)(25,32,36,50)(27,28,45,48)(29,41,30,40)(33,46,37,55)(34,52,53,51)(35,54,49,43)(38,39,47,44);(24,27,31,45)(25,33,36,37)(26,38,42,47)(28,40,48,41)(29,39,30,44)(32,34,50,53)(35,52,49,51)(43,55,54,46)

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, 6321);