C₁₉×#1967 #14559824

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×#1967

Subgroups

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

312 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 608

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)(24,25,28,31,27,30,34,36)(26,29,33,38,32,37,35,39);(24,26,28,35,27,32,34,33)(25,29,36,38,30,37,31,39);(20,21,22,23)(25,30)(29,37)(31,36)(38,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8483, C₁₉×#8484, C₁₉×#10496, …
maximal normal subgroup of	C₁₉×#8483, C₁₉×#8484, C₁₉×#10496, …
maximal quotient of	C₁₉×#9651, C₁₉×#9652, C₁₉×#9687, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 699);