C₁₉×#2081 #14559938

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2081
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2081

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#397
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

204 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 72 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)(20,21,24,26,25,29,23,28)(22,30,32,35,31,34,33,27);(21,26)(22,31)(23,24)(27,34)(28,29)(30,35);(20,22,23,32,25,31,24,33)(21,27,28,30,29,35,26,34)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2081, C₁₉×#23652, C₁₉×#24987, …
maximal normal subgroup of	C₂×C₁₉×#2081, C₁₉×#23652, C₁₉×#24987, …
maximal quotient of	C₁₉×#10631, C₁₉×#10633, C₁₉×#10634, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 813);