C₃×#1055 #64588

order	312
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂³×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = D₁₃ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₁₃ ⋊ C₃×C₈
Hall	C₃×C₁₃ ⋊ C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 312

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 4);