C₂×C₁₉×#421 #14560757

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×#421

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×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

772 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);(3,4,7,10,8,11,6,15)(5,12,14,9,13,18,16,17);(3,5)(4,9)(6,16)(7,14)(8,13)(10,18)(11,17)(12,15);(5,13)(9,17)(12,18)(14,16)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10772, C₁₉×#10773, C₁₉×#10775, …
maximal normal subgroup of	C₁₉×#10772, C₁₉×#10773, C₁₉×#10775, …
maximal quotient of	C₂×C₁₉×#1478, C₂×C₁₉×#1479, C₂×C₁₉×#1477, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1632);

C2×C19×#421 #14560757

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#421 #14560757