C₁₉×#9989 #18015948

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#9989

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

724 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 2977);