C₁₉×#1495 #14559352

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1495

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₁₉×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 216 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)(22,26)(25,27)(28,29,31,35,32,34,38,41)(30,33,37,39,36,40,42,43);(20,21)(22,27)(23,25)(24,26)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(21,25)(24,27)(29,34)(30,36)(35,41)(37,42)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8483, C₁₉×#8484, C₁₉×#8485, …
maximal normal subgroup of	C₁₉×#8483, C₁₉×#8484, C₁₉×#8485, …
maximal quotient of	C₁₉×#7694, C₁₉×#7695, C₁₉×#7696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 227);