C₂×C₁₉×#1459 #18023305

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₁₉ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₁₉×#1459

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂³×C₈×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₁₉	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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)(5,9,10,7)(6,8)(11,12,14,17,15,18,13,16);(3,5)(4,7)(6,10)(8,9);(11,13,15,14)(12,16,18,17)

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 10334);

C2×C19×#1459 #18023305

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₂×C₁₉×#1459 #18023305