C₂×C₁₉×#419 #14560751

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₉×#419

Subgroups

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

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4,5,6)(7,8)(9,16)(10,14)(11,20)(12,15)(13,18)(17,21)(19,22);(7,9,12,19)(8,13,15,21)(10,18,11,17)(14,22,20,16);(7,10,12,11)(8,14,15,20)(9,17,19,18)(13,16,21,22)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10777, C₁₉×#10786, C₁₉×#10942, …
maximal normal subgroup of	C₁₉×#10777, C₁₉×#10786, C₁₉×#10942, …
maximal quotient of	C₂×C₁₉×#1479, C₂×C₁₉×#1491, C₁₉×#17449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1626);

C2×C19×#419 #14560751

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#419 #14560751