C₁₉×#2062 #14559919

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2062

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

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

normal subgroups only

This group has 314 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) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12226, C₁₉×#12227, C₁₉×#12228, …
maximal normal subgroup of	C₁₉×#12226, C₁₉×#12227, C₁₉×#12228, …
maximal quotient of	C₁₉×#10567, C₁₉×#10568, C₁₉×#10569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 794);