C₁₉×#2724 #14560581

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2724

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

504 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 192 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)(26,30)(27,28)(29,31)(32,33,36,38)(34,39,35,37);(21,23)(25,28)(26,31)(32,34,36,35)(33,37,38,39);(20,21)(22,23)(24,26)(25,29)(27,31)(28,30)(32,35,36,34)(33,37,38,39);(24,25)(26,29)(27,28)(30,31)(32,33)(34,39)(35,37)(36,38)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7736, C₁₉×#7751, C₁₉×#7770, …
maximal normal subgroup of	C₁₉×#7736, C₁₉×#7751, C₁₉×#7770, …
maximal quotient of	C₁₉×#14384, C₁₉×#14440, C₁₉×#14446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1456);