C₂×C₁₉×#444 #14560811

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×#444

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

464 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);(3,4,7,11,8,5,12,10)(6,13,14,17,15,9,16,18);(3,5)(4,8)(6,13)(7,10)(9,15)(11,12)(14,17)(16,18);(3,6,7,14,8,15,12,16)(4,9,11,18,5,13,10,17)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12650, C₁₉×#12651, C₁₉×#12944, …
maximal normal subgroup of	C₁₉×#12650, C₁₉×#12651, C₁₉×#12944, …
maximal quotient of	C₂×C₁₉×SD₁₆⋊C₈, C₂×C₁₉×#1579, C₂×C₁₉×#1580, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1686);

C2×C19×#444 #14560811

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#444 #14560811