C₁₉×#1814 #14559671

order	2432
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1814

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#121
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#380
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

256 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 116 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)(22,31)(23,36,38,43)(24,39)(25,29)(26,30)(27,33)(28,37,44,40)(32,41,48,51)(34,42)(35,46)(45,47,50,49);(20,22,24,33,26,35,25,34)(21,27,29,31,30,42,39,46)(23,32,37,47,38,48,40,49)(28,41,43,45,44,51,36,50);(20,23)(21,28)(22,32)(24,37)(25,40)(26,38)(27,41)(29,43)(30,44)(31,45)(33,47)(34,49)(35,48)(36,39)(42,51)(46,50)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12747, C₁₉×#12750, C₁₉×#12751, …
maximal normal subgroup of	C₁₉×#12747, C₁₉×#12750, C₁₉×#12751, …
maximal quotient of	C₁₉×#8604, C₁₉×#8605, C₁₉×#8606, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 546);