C₁₉×#1511 #14559368

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1511

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 274 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) = 608

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)(20,21)(22,26,27,24)(23,25)(28,29)(30,36,38,43)(31,35)(32,34)(33,37,41,39)(40,42);(20,22,23,27)(21,24,25,26)(28,30)(29,33)(31,39)(32,38)(34,41)(35,43)(36,42)(37,40);(29,34)(33,41)(35,42)(36,43)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8488, C₁₉×#8517, C₁₉×#8519, …
maximal normal subgroup of	C₁₉×#8488, C₁₉×#8517, C₁₉×#8519, …
maximal quotient of	C₁₉×#7593, C₁₉×#7595, C₁₉×#7600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 243);