C₁₉×#3306 #14561163

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3306

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#3306, C₁₉×#61141, C₁₉×#61156, …
maximal normal subgroup of	C₂×C₁₉×#3306, C₁₉×#61141, C₁₉×#61156, …
maximal quotient of	C₁₉×#22419, C₁₉×#22495, C₁₉×#22562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2038);

C19×#3306 #14561163

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3306 #14561163