C₂₃×AGL(1,𝔽₈) #13046248

order	1288
isoclinism	isoclinic class of AGL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₇×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

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

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

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

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 184

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26,27,29,31,28,30);(24,28)(25,26)(27,31)(29,30)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1288, 30);