C₂×D₄×C₅²⋊C₃ #11925666

order	1200
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₅

Aliases

direct product	C₂×D₄×C₅²⋊C₃
unambiguous semidirect product	C₄⋊(C₂²×C₅²⋊C₃)
unambiguous semidirect product	(C₂×C₅²×D₄)⋊C₃

Fitting, Hall	C₂×C₅²×D₄ ⋊ C₃
Sylow	C₅² ⋊ C₂×C₃×D₄

162 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 876);