C₁₉×#1489 #14559346

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1489

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#41×C₁₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

266 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 104 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 — 3 generators on 35 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8440, C₁₉×#8441, C₁₉×#8442, …
maximal normal subgroup of	C₁₉×#8440, C₁₉×#8441, C₁₉×#8442, …
maximal quotient of	C₁₉×#7612, C₁₉×#7613, C₁₉×#7614, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 221);