C₁₉×#2038 #14559895

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2038

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

278 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 84 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)(21,22)(24,25)(26,29)(27,30)(28,32)(31,36)(33,37)(34,39)(35,38);(20,21)(22,23)(24,26,28,34)(25,29,32,39)(27,35,36,33)(30,38,31,37);(20,22,23,21)(25,30)(27,36)(29,37)(31,32)(33,35)(38,39)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2038, C₁₉×#23492, C₁₉×#23494, …
maximal normal subgroup of	C₂×C₁₉×#2038, C₁₉×#23492, C₁₉×#23494, …
maximal quotient of	C₁₉×#10396, C₁₉×#10397, C₁₉×#10400, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 770);