C₁₉×#32948 #18038907

order	4864
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₉×#32948

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

1334 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 290 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)(21,26)(24,27)(28,36)(29,37)(30,38)(31,44)(32,39)(34,40)(41,50)(42,47)(43,48)(46,51);(20,21,27,38,25,30,24,26)(22,28,39,47,33,42,32,36)(23,29,40,48,35,43,34,37)(31,41,49,50,44,51,45,46);(20,22)(21,28)(23,31)(24,32)(25,33)(26,36)(27,39)(29,41)(30,42)(34,45)(35,44)(37,46)(38,47)(40,49)(43,51)(48,50);(20,23)(21,29)(22,31)(24,34)(25,35)(26,37)(27,40)(28,41)(30,43)(32,45)(33,44)(36,46)(38,48)(39,49)(42,51)(47,50)

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, 25936);