C₁₉×#11432 #18017391

order	4864
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#11432

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄⋊C₄×C₁₉ ◁ G

594 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 142 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)(30,36,37,43)(31,39,41,34)(32,35)(33,38)(40,42);(28,30)(29,33)(31,40)(32,37)(34,43)(35,42)(36,39)(38,41);(30,37)(33,42)(36,43)(38,40)

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, 4420);