C₂₇×AGL(1,𝔽₈) #13094186

order	1512
isoclinism	isoclinic class of AGL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₇×C₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₇×AGL(1,𝔽₈)
unambiguous semidirect product	(C₂³×C₂₇)⋊C₇

Fitting, Hall	C₂³×C₂₇ ⋊ C₇
derived, Sylow	C₂³ ⋊ C₇×C₂₇

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 2 generators on 35 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)(29,30,31,33,35,32,34);(28,32)(29,30)(31,35)(33,34)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 83);