ΓL(1,𝔽₂₅) #203

order	48
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂³×D₃ (order 48) · Inn(G) = C₂×D₃ · Out(G) = C₂²
holomorph	G ⋊ Aut(G) = #72213893
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

Aliases

ΓL(1,𝔽₂₅)

Fitting	C₃×C₈ ⋊ C₂
Sylow	C₃ ⋊ M₁₆

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 11 points:

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

Polycyclic presentation:

2^4,3|b^2=c,c^2=d,b^a=bd,e^a=e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 5);