C₁₉×#2007 #14559864

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2007

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

370 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 92 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)(24,25,29,33)(26,34,36,39)(27,32,28,31)(30,37,38,35);(20,21)(22,23)(24,26)(25,30)(27,37)(28,35)(29,36)(31,39)(32,34)(33,38);(21,23)(24,26)(25,30)(27,35)(28,37)(29,36)(31,34)(32,39)(33,38)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7409, C₁₉×#12098, C₁₉×#12100, …
maximal normal subgroup of	C₁₉×#7409, C₁₉×#12098, C₁₉×#12100, …
maximal quotient of	C₁₉×#9934, C₁₉×#9935, C₁₉×#9936, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 739);