C₁₉×#1966 #14559823

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1966

Subgroups

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

292 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,27,31,28,30,32,38)(26,29,34,36,33,37,35,39);(24,26,32,34,28,33,27,35)(25,29,31,39,30,37,38,36);(20,21,22,23)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8470, C₁₉×#8473, C₁₉×#9251, …
maximal normal subgroup of	C₁₉×#8470, C₁₉×#8473, C₁₉×#9251, …
maximal quotient of	C₁₉×#9650, C₁₉×#9654, C₁₉×#9686, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 698);