C₁₉×#1400 #14559257

order	2432
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1400

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	C₂²⋊C₁₆
prime radical	C₂³×C₁₉	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ G

74 conjugacy classes of subgroups.

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7336, C₁₉×#7337, C₁₉×#7364, …
maximal normal subgroup of	C₁₉×#7336, C₁₉×#7337, C₁₉×#7364, …
maximal quotient of	C₁₉×#7334, C₁₉×#7362, C₁₉×#7380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 132);

C19×#1400 #14559257

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1400 #14559257