C₁₉×#11394 #18017353

order	4864
nilpotency class	3
isoclinism	isoclinic class of #2032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#11394

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 39 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)(26,29,33,37)(27,34)(28,31)(30,35)(32,38,39,36);(21,23)(24,26)(25,29,31,37)(27,32)(28,33)(30,38,34,36)(35,39);(24,27)(25,30,31,34)(26,32)(28,35)(29,36,37,38)(33,39)

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, 4382);