C₁₉×#20340 #18026299

order	4864
nilpotency class	2
isoclinism	isoclinic class of #20338
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₉×#20340

Subgroups

	subgroup	G/H
center	C₄×C₁₉	C₂²×C₄²
commutator	C₄	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂²×#95
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ G

1956 conjugacy classes of subgroups; only the 1114 normal subgroups are shown.

normal subgroups only

This group has 1956 conjugacy classes of subgroups — too many to draw. Only its 1114 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 51 points:

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

Conjugacy classes & character table

1558 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 13328);