C₁₉×#1529 #14559386

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×#1529

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₁₉×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

216 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 88 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)(28,29,32,35,33,36,31,40)(30,37,38,42,39,34,41,43);(20,21)(22,26)(23,25)(24,27)(28,30)(29,34)(31,38)(32,41)(33,39)(35,42)(36,37)(40,43);(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,37,43)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8412, C₁₉×#8413, C₁₉×#8414, …
maximal normal subgroup of	C₁₉×#8412, C₁₉×#8413, C₁₉×#8414, …
maximal quotient of	C₁₉×#7574, C₁₉×#7577, C₁₉×#7582, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 261);