C₁₉×#3295 #14561152

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3295

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	D₄²×C₁₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

462 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)(28,29,31,34)(30,32,35,33);(20,22)(21,24)(23,27)(25,26);(29,32)(30,35)(33,34);(22,27)(24,26)

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#19763, C₁₉×#19765, C₁₉×#19773, …
maximal normal subgroup of	C₁₉×#19763, C₁₉×#19765, C₁₉×#19773, …
maximal quotient of	D₄×C₁₉×#102, C₁₉×#22487, C₁₉×#22574, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2027);

C19×#3295 #14561152

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3295 #14561152