C₃²×AGL(1,𝔽₈) #92747

order	504
isoclinism	isoclinic class of AGL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×AGL(1,𝔽₈)
unambiguous semidirect product	(C₂³×C₃²)⋊C₇

Fitting, socle, Hall	C₂³×C₃² ⋊ C₇
derived, Sylow	C₂³ ⋊ C₃²×C₇

	subgroup	G/H
center, hypercenter	C₃²	AGL(1,𝔽₈)
commutator, cosocle, hypocenter	C₂³	C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₂³×C₃²	C₇
LCS	G ▷ C₂³
UCS	C₁ ◁ C₃²

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 173);