C₁₉×#19078 #18025037

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#19078

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

944 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 2432

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

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 12066);