C₂×C₁₉×#482 #14560944

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₁₉×#482

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

468 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)(5,8)(6,7)(9,10)(12,15)(13,16)(17,18);(4,7)(8,10)(11,12,14,15)(13,16,17,18);(3,5,6,9)(4,8,7,10)(11,13,14,17)(12,16,15,18)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9242, C₄×C₁₉×#482, C₁₉×#21582, …
maximal normal subgroup of	C₁₉×#9242, C₄×C₁₉×#482, C₁₉×#21582, …
maximal quotient of	C₂×C₁₉×#1825, C₂×C₁₉×#1854, C₂×C₁₉×#1875, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1819);

C2×C19×#482 #14560944

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#482 #14560944