C₁₉×#3298 #14561155

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×#3298

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

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);(28,29,31,33)(30,35,34,32);(22,27)(24,26)

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#19766, C₁₉×#19767, C₁₉×#19779, …
maximal normal subgroup of	C₁₉×#19766, C₁₉×#19767, C₁₉×#19779, …
maximal quotient of	D₄×C₁₉×#103, C₁₉×#22485, C₁₉×#22571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2030);

C19×#3298 #14561155

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3298 #14561155