C₁₉×#2542 #14560399

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#2542

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9395, C₁₉×#9403, C₁₉×#9455, …
maximal normal subgroup of	C₁₉×#9395, C₁₉×#9403, C₁₉×#9455, …
maximal quotient of	C₁₉×#13906, C₁₉×#13910, C₁₉×#13977, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1274);

C19×#2542 #14560399

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2542 #14560399