C₂×C₃×Dic₁₉ #90707

order	456
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×Dic₁₉

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

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 456

A minimal faithful permutation representation — 2 generators on 28 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 27);