C₁₉×#3152 #14561009

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#3152

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

552 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 224 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 — 4 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)(26,32,33,39)(27,35,36,30)(29,37,38,34);(24,26,27,34,28,33,36,37)(25,29,30,32,31,38,35,39);(20,21,22,23);(26,33)(29,38)(32,39)(34,37)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9421, C₁₉×#9429, C₁₉×#9435, …
maximal normal subgroup of	C₁₉×#9421, C₁₉×#9429, C₁₉×#9435, …
maximal quotient of	C₁₉×#19622, C₁₉×#19626, C₁₉×#19630, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1884);