C₂×C₈×C₁₉⋊C₃ #11744840

order	912
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₈×C₁₉⋊C₃
unambiguous semidirect product	(C₂×C₈×C₁₉)⋊C₃

Fitting, Hall	C₂×C₈×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂×C₃×C₈

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2)(12,13,15)(14,17,18)(16,20,19)(21,25,23)(22,26,24)(27,29,28);(3,4,5,6,7,8,9,10)(11,12,14,18,23,28,25,13,16,21,26,15,19,24,17,22,27,29,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 51);