C₁₉×#1485 #14559342

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1485

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	C₂³×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

218 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 96 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)(20,21,24,27,25,22,23,26)(28,29)(30,37)(31,35)(32,41)(33,36)(34,39)(38,42)(40,43);(20,22,25,21)(23,27,24,26)(28,30,33,40)(29,34,36,42)(31,39,32,38)(35,43,41,37);(20,23,25,24)(21,26,22,27)(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,37,42,43)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8413, C₁₉×#8415, C₁₉×#8484, …
maximal normal subgroup of	C₁₉×#8413, C₁₉×#8415, C₁₉×#8484, …
maximal quotient of	C₁₉×#7675, C₁₉×#7680, C₁₉×#7682, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 217);