C₁₉×#1584 #14559441

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1584

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle, prime radical	C₂²×C₁₉	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

152 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 88 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 — 3 generators on 43 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1584, C₁₉×#17863, C₁₉×#17870, …
maximal normal subgroup of	C₂×C₁₉×#1584, C₁₉×#17863, C₁₉×#17870, …
maximal quotient of	C₁₉×#8203, C₁₉×#8211, C₁₉×#8291, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 316);