C₄×Dic₁₉ #64521

order	304
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product	C₄×Dic₁₉
unambiguous semidirect product	C₁₉⋊C₄²

C₁₉ ⋊ C₄²

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 2 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(304, 10);