C₁₉×#1605 #14559462

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1605

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 68 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)(24,27)(28,29,32,35)(30,36,38,43)(31,39,41,34)(33,40,42,37);(20,21)(22,24)(23,25)(26,27)(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36);(20,22,23,26)(21,24,25,27)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12220, C₁₉×#12222, C₁₉×#12223, …
maximal normal subgroup of	C₁₉×#12220, C₁₉×#12222, C₁₉×#12223, …
maximal quotient of	C₁₉×#7757, C₁₉×#7761, C₁₉×#7763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 337);