C₁₉×#1287 #14559144

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#1287

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#95
commutator	C₂×C₄	C₄²×C₁₉
Frattini, cosocle	C₂×C₄²	C₂²×C₁₉
prime radical	C₂³×C₁₉	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 1216

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)(20,21,23,28,25,29,24,27)(22,30,31,26,33,34,32,35)(36,37)(38,44,46,50)(39,42)(40,43)(41,45,48,51)(47,49);(20,22,24,32,25,33,23,31)(21,26,28,34,29,35,27,30)(36,38)(37,41,43,48)(39,45)(40,46)(42,44,49,50)(47,51)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1287, C₁₉×#7964, C₁₉×#7965, …
maximal normal subgroup of	C₂×C₁₉×#1287, C₁₉×#7964, C₁₉×#7965, …
maximal quotient of	C₁₉×#7018, C₁₉×#7021, C₁₉×#7023, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19);