C₁₉×#1388 #14559245

order	2432
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1388

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#102
commutator	C₈	C₄²×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂×C₁₉	#340
prime radical	C₂³×C₁₉	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

124 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 76 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 — 2 generators on 51 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1388, C₁₉×#12646, C₁₉×#12651, …
maximal normal subgroup of	C₂×C₁₉×#1388, C₁₉×#12646, C₁₉×#12651, …
maximal quotient of	C₁₉×#7158, C₁₉×#7176, C₁₉×#7177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 120);