C₁₉×#2889 #14560746

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#2889

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×2₋¹⁺⁴	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

704 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 generators on 51 points:

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

Conjugacy classes & character table

779 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13096, C₁₉×#13098, C₁₉×#21780, …
maximal normal subgroup of	C₁₉×#13096, C₁₉×#13098, C₁₉×#21780, …
maximal quotient of	C₁₉×#17351, C₁₉×#17352, C₁₉×#17368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1621);