C₁₉×#11993 #18017952

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11992
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11993

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1555
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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)(20,21,23,29,24,28,37,44,25,27,36,43,39,30,47,46)(22,31,32,48,33,40,50,51,34,42,49,45,38,26,35,41);(20,22,25,34)(21,26,27,40)(23,35,36,50)(24,38,39,33)(28,42,30,31)(29,45,43,48)(32,37,49,47)(41,44,51,46);(21,27)(23,36)(26,40)(28,30)(31,42)(32,49)(35,50)(37,47)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4981);