C₁₉×#3184 #14561041

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#3184

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 ◁ C₂×C₄²×C₁₉ ◁ G

446 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9417, C₁₉×#11837, C₁₉×#18554, …
maximal normal subgroup of	C₁₉×#9417, C₁₉×#11837, C₁₉×#18554, …
maximal quotient of	C₁₉×#20824, C₁₉×#21286, C₁₉×#21410, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1916);