C₂×D₃×D₁₉ #90727

order	456
isoclinism	isoclinic class of D₃×D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₃×D₁₉
unambiguous semidirect product	(D₃×C₁₉)⋊C₂²
unambiguous semidirect product	(C₃×D₁₉)⋊C₂²
unambiguous semidirect product	D₅₇⋊C₂²

	subgroup	G/H
center, hypercenter	C₂	D₃×D₁₉
commutator, cosocle, hypocenter	C₃×C₁₉	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 114

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2)(3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24);(4,5)(6,7,9,11,13,15,17,19,21,23,24,22,20,18,16,14,12,10,8);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 47);