C₂×C₁₉×#413 #14560744

order	2432
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₉×#413

Subgroups

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

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 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);(3,4,7,12,8,11,6,10)(5,13,14,18,15,9,16,17);(3,5)(4,9)(6,14)(7,16)(8,15)(10,17)(11,13)(12,18);(3,6,8,7)(4,10,11,12)(5,14,15,16)(9,17,13,18)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10744, C₁₉×#10746, C₁₉×#10747, …
maximal normal subgroup of	C₁₉×#10744, C₁₉×#10746, C₁₉×#10747, …
maximal quotient of	C₂×C₁₉×#1458, C₂×C₁₉×#1459, C₁₉×#17349, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1619);

C2×C19×#413 #14560744

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#413 #14560744