C₁₉×#2032 #14559889

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2032
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2032

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#393
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 304

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2032, C₁₉×#23474, C₁₉×#23996, …
maximal normal subgroup of	C₂×C₁₉×#2032, C₁₉×#23474, C₁₉×#23996, …
maximal quotient of	C₁₉×#10374, C₁₉×#10375, C₁₉×#10376, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 764);