C₂³×ΓL(1,𝔽₂₅) #87146

order	384
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Fitting	C₂³×C₃×C₈ ⋊ C₂
Sylow	C₃ ⋊ C₂³×M₁₆

1720 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 5 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19722);