C₁₉×#1922 #14559779

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

Aliases

direct product

C₁₉×#1922

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 186 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) = 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)(22,25)(23,24)(26,27)(28,29,32,36,33,31,40,35)(30,34,38,42,39,37,43,41);(21,24)(25,27)(28,30,32,38,33,39,40,43)(29,34,36,42,31,37,35,41);(20,22,23,26)(21,25,24,27)(28,31)(29,33)(30,37)(32,35)(34,39)(36,40)(38,41)(42,43)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1922, C₁₉×#21041, C₁₉×#21042, …
maximal normal subgroup of	C₂×C₁₉×#1922, C₁₉×#21041, C₁₉×#21042, …
maximal quotient of	C₁₉×#9533, C₁₉×#9534, C₁₉×#9535, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 654);