C₂×C₁₉×#544 #14561314

order	2432
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₁₉×#544

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 5 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4)(5,9)(6,8)(7,10)(11,12,14,16)(13,17,18,15);(3,4,6,8)(5,7,10,9);(3,4)(5,7)(6,8)(9,10)(11,13,14,18)(12,15,16,17);(3,5)(4,7)(6,10)(8,9)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8406, C₁₉×#8525, C₁₉×#11388, …
maximal normal subgroup of	C₁₉×#8406, C₁₉×#8525, C₁₉×#11388, …
maximal quotient of	C₂×C₁₉×#2316, C₂×C₁₉×#2317, C₂×C₁₉×#2329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2189);

C2×C19×#544 #14561314

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#544 #14561314