C₂×C₄×C₁₉⋊C₃ #90699

order	456
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₄×C₁₉⋊C₃
unambiguous semidirect product	(C₂×C₄×C₁₉)⋊C₃

Fitting, Hall	C₂×C₄×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂×C₃×C₄

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 152

A minimal faithful permutation representation — 2 generators on 25 points:

(3,4,5,6)(8,9,11)(10,13,14)(12,16,15)(17,21,19)(18,22,20)(23,25,24);(1,2)(7,8,10,14,19,24,21,9,12,17,22,11,15,20,13,18,23,25,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 19);