C₂₅×AGL(1,𝔽₈) #13063744

order	1400
isoclinism	isoclinic class of AGL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₇×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×AGL(1,𝔽₈)
unambiguous semidirect product	C₂³⋊(C₇×C₂₅)
unambiguous semidirect product	(C₂³×C₂₅)⋊C₇

Fitting, Hall	C₂³×C₂₅ ⋊ C₇
derived, Sylow	C₂³ ⋊ C₇×C₂₅

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 2 generators on 33 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)(27,28,29,31,33,30,32);(26,30)(27,28)(29,33)(31,32)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 33);