C₁₉×#13076 #18019035

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13076

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3060	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

466 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 146 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 — 3 generators on 51 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6064);