Dic₃×C₂₅ #64458

order	300
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×C₄×C₅×D₃ (order 240) · Inn(G) = D₃ · Out(G) = C₂×C₄×C₅
homology	Abelianization (H₁) = C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₂₅
unambiguous semidirect product	C₃⋊(C₄×C₂₅)

derived, Sylow	C₃ ⋊ C₄×C₂₅
Hall	C₃×C₂₅ ⋊ C₄

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 300

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(1,3,2,4)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 1);