C₁₉×#2629 #14560486

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2629

Subgroups

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

472 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 216 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)(24,25)(26,28)(27,29)(30,31)(32,33,36,35)(34,38,39,37);(21,23)(25,26)(29,30)(32,34)(33,37)(35,38)(36,39);(20,21)(22,23)(24,26,28,25)(27,29,31,30)(32,34)(33,38)(35,37)(36,39);(24,27,28,31)(25,29,26,30)(32,35,36,33)(34,38,39,37)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#24713, C₁₉×#24715, C₁₉×#24717, …
maximal normal subgroup of	C₁₉×#24713, C₁₉×#24715, C₁₉×#24717, …
maximal quotient of	C₁₉×#14264, C₁₉×#14266, C₁₉×#14276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1361);