C₁₉×#1401 #14559258

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1401

Subgroups

	subgroup	G/H
center	C₁₆×C₁₉	D₄
commutator	C₄	C₂×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₉
socle	C₂×C₁₉	C₂²⋊C₁₆
prime radical	#41×C₁₉	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,25,31,43,56,26,32,44,57,46,59,71,79,27,33,45,58,47,60,72,80,23,29,40,53,41,54,68,77)(22,34,36,61,37,62,65,81,35,51,63,55,64,75,82,78,38,52,42,69,66,76,70,83,39,28,48,49,67,50,73,74);(20,22)(21,28)(23,39)(24,42)(25,37)(26,35)(27,38)(29,52)(30,55)(31,50)(32,34)(33,51)(36,45)(40,63)(41,67)(43,70)(44,48)(46,64)(47,66)(49,58)(53,61)(54,76)(56,78)(57,69)(59,62)(60,75)(65,72)(68,82)(71,73)(74,80)(77,81)(79,83)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₉×#1401, C₁₉×#13558, C₁₉×#13647, …
maximal normal subgroup of	C₂×C₁₉×#1401, C₁₉×#13558, C₁₉×#13647, …
maximal quotient of	C₁₉×#7335, C₁₉×#7363, C₁₉×D₄⋊C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 133);

C19×#1401 #14559258