C₁₉×#2122 #14559979

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#2122

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#99
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂³×C₁₉
prime radical	C₁₉×#535	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

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

normal subgroups only

This group has 266 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) = 35
transitive degree	μ_t(G) = 304

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12715, C₁₉×#12718, C₁₉×#12721, …
maximal normal subgroup of	C₁₉×#12715, C₁₉×#12718, C₁₉×#12721, …
maximal quotient of	C₁₉×#11427, C₁₉×#11454, C₁₉×#11473, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 854);