C₁₉×#1995 #14559852

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1995

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

244 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 112 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 — 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)(22,26)(23,24)(25,27)(28,29,32,35,33,36,31,41)(30,37,40,42,38,43,39,34);(21,24)(25,26)(28,30)(29,34,36,42)(31,39)(32,40)(33,38)(35,37,41,43);(20,22,23,27)(21,25,24,26)(30,38)(34,42)(37,43)(39,40)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7129, C₁₉×#7360, C₁₉×#8494, …
maximal normal subgroup of	C₁₉×#7129, C₁₉×#7360, C₁₉×#8494, …
maximal quotient of	C₁₉×#9872, C₁₉×#9873, C₁₉×#9874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 727);