C₁₉×#1528 #14559385

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1528

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 212 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24,25,26)(28,29,31,35,32,34,40,42)(30,36,37,43,38,33,39,41);(20,21)(22,26)(23,25)(24,27)(28,30,32,38)(29,33,34,36)(31,39,40,37)(35,43,42,41);(29,34)(33,36)(35,42)(41,43)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8371, C₁₉×#8372, C₁₉×#8373, …
maximal normal subgroup of	C₁₉×#8371, C₁₉×#8372, C₁₉×#8373, …
maximal quotient of	C₁₉×#7573, C₁₉×#7576, C₁₉×#7585, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 260);