C₂×C₁₉×#430 #14560772

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₁₉×#430

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

460 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);(3,4,7,10,8,11,6,16)(5,12,15,17,13,18,14,9);(3,5,6,14,8,13,7,15)(4,9,10,12,11,17,16,18);(5,13)(9,17)(12,18)(14,15)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10897, C₁₉×#10898, C₁₉×#10901, …
maximal normal subgroup of	C₁₉×#10897, C₁₉×#10898, C₁₉×#10901, …
maximal quotient of	C₂×C₁₉×#1565, C₁₉×#17787, C₂×C₁₉×#1569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1647);

C2×C19×#430 #14560772

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#430 #14560772