C₁₉×#1334 #14559191

order	2432
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1334

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2432

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)(20,21,22,24,23,25,26,27)(29,33,34,41)(30,36)(31,39)(35,37,40,42)(38,43);(28,29,32,34)(30,37,38,42)(31,40,39,35)(33,36,41,43)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1334, C₁₉×#11597, C₁₉×#11598, …
maximal normal subgroup of	C₂×C₁₉×#1334, C₁₉×#11597, C₁₉×#11598, …
maximal quotient of	C₁₉×#7071, C₁₉×#7075, C₁₉×#7113, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 66);

C19×#1334 #14559191

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1334 #14559191