C₃×#87837 #11925394

order	1200
isoclinism	isoclinic class of #87837
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₅² ⋊ D₈
Sylow	C₅² ⋊ C₃×D₈

84 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 604);