C₁₉×#2231 #14560088

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2231

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#476
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,31)(22,32,35,30)(23,36)(24,40,33,29)(25,27,42,44)(28,45)(34,48)(37,50)(38,49)(39,43)(41,46)(47,51);(20,22,33,42,26,35,24,25)(21,27,40,30,31,44,29,32)(23,34,38,51,39,45,37,41)(28,43,47,49,48,36,46,50);(20,23)(21,28)(22,34)(24,37)(25,41)(26,39)(27,43)(29,46)(30,49)(31,48)(32,50)(33,38)(35,45)(36,44)(40,47)(42,51)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12463, C₁₉×#12464, C₁₉×#12465, …
maximal normal subgroup of	C₁₉×#12463, C₁₉×#12464, C₁₉×#12465, …
maximal quotient of	C₁₉×#12824, C₁₉×#12950, C₁₉×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 963);