C₁₉×#1612 #14559469

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1612

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#538	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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)(21,25)(22,23)(26,27)(28,29,32,35)(30,33,37,40)(31,34,38,41)(36,42,43,39);(20,21)(22,25)(23,27)(24,26)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42);(20,22,24,23)(21,25,26,27)(28,31,32,38)(29,34,35,41)(30,36,37,43)(33,39,40,42)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1612, C₁₉×#18121, C₁₉×#18126, …
maximal normal subgroup of	C₂×C₁₉×#1612, C₁₉×#18121, C₁₉×#18126, …
maximal quotient of	C₁₉×#7795, C₁₉×#7796, C₁₉×#7799, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 344);