C₁₉×#1617 #14559474

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1617

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

202 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,41)(22,31,33,48)(23,36,42,38)(24,29,25,30)(27,43,44,32)(28,40,51,39)(34,47,35,49)(37,45,50,46);(20,22,24,34)(21,27,29,45)(23,37,39,32)(25,35,26,33)(28,47,36,31)(30,46,41,44)(38,48,51,49)(40,43,42,50);(20,21,25,30)(22,27,35,46)(23,38,40,28)(24,29,26,41)(31,32,49,50)(33,44,34,45)(36,39,51,42)(37,48,43,47)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12221, C₁₉×#12222, C₁₉×#12223, …
maximal normal subgroup of	C₁₉×#12221, C₁₉×#12222, C₁₉×#12223, …
maximal quotient of	C₁₉×#7792, C₁₉×#7794, C₁₉×#7806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 349);