D₅×#125 #66021

order	320
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₅×#125 ⋊ C₂
Sylow	C₅ ⋊ C₂×#125

226 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1359);