C₂×C₁₉×H(3,ℤ/4) #14559587

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₁₉×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₄²
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#95
prime radical	C₂⁴×C₁₉	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 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)(5,11,13,17)(6,9)(7,10)(8,12,15,18)(14,16);(3,5)(4,8,10,15)(6,12)(7,13)(9,11,16,17)(14,18)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7254, C₁₉×#7256, C₄×C₁₉×H(3,ℤ/4), …
maximal normal subgroup of	C₁₉×#7254, C₁₉×#7256, C₄×C₁₉×H(3,ℤ/4), …
maximal quotient of	C₂×C₁₉×#1274, C₁₉×#7854, C₁₉×#7855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 462);

C2×C19×H(3,ℤ/4) #14559587

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×H(3,ℤ/4) #14559587