C₂×C₁₉×#410 #14560739

order	2432
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₁₉×#410

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂³	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

788 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)(5,11,13,8)(6,9)(7,10)(12,17,18,15)(14,16);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10742, C₁₉×#10743, C₁₉×#10748, …
maximal normal subgroup of	C₁₉×#10742, C₁₉×#10743, C₁₉×#10748, …
maximal quotient of	C₂×C₁₉×#1458, C₂×C₁₉×#1460, C₂×C₁₉×#1461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1614);

C2×C19×#410 #14560739

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#410 #14560739