C₁₉×#1290 #14559147

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1290

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

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7080, C₁₉×#7081, C₁₉×#7082, …
maximal normal subgroup of	C₁₉×#7080, C₁₉×#7081, C₁₉×#7082, …
maximal quotient of	C₁₉×#7020, C₁₉×#7023, C₁₉×#7038, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 22);

C19×#1290 #14559147

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1290 #14559147