C₁₉×#21795 #18027754

order	4864
nilpotency class	3
isoclinism	isoclinic class of #17405
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₉×#21795

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#534	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₂²⋊C₄×C₁₉ ◁ G

1538 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 366 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) = 608

A minimal faithful permutation representation — 4 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)(22,26)(23,25)(24,27)(28,29)(30,33)(31,38,39,34)(32,35)(36,42,43,40)(37,41);(20,22,23,27)(21,24,25,26)(28,30)(29,33)(31,36)(32,37)(34,40)(35,41)(38,42)(39,43);(22,27)(24,26)(28,31)(29,34)(30,36)(32,39)(33,40)(35,38)(37,43)(41,42);(21,25)(24,26)(30,37)(33,41)(36,43)(40,42)

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, 14783);