C₁₉×#1599 #14559456

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

Aliases

direct product

C₁₉×#1599

Subgroups

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

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

normal subgroups only

This group has 266 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) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 35 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)(32,35);(20,21,23,25)(22,27,26,24)(28,29)(30,32)(31,33)(34,35);(28,30,31,34)(29,32,33,35)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12208, C₁₉×#12210, C₁₉×#12211, …
maximal normal subgroup of	C₁₉×#12208, C₁₉×#12210, C₁₉×#12211, …
maximal quotient of	C₁₉×#7739, C₁₉×#7741, C₁₉×#7747, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 331);