ΓL(2,𝔽₈) #72224448

order	10584
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

ΓL(2,𝔽₈)

Fitting	C₇ ⋊ ΣL(2,𝔽₈)
socle, derived	C₇×SL(2,𝔽₈) ⋊ C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, cosocle, hypocenter	C₇×SL(2,𝔽₈)	C₃
Fitting	C₇	ΣL(2,𝔽₈)
LCS	G ▷ C₇×SL(2,𝔽₈)
UCS	C₁

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 63

A minimal faithful permutation representation — 2 generators on 16 points:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,3,5)(2,6,7)(8,11,12)(13,15,14), (1,2,3,5,4,7,6)(9,10,11,14,13,16,15));