C₃×#1057 #64597

order	312
isoclinism	isoclinic class of #261
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₃) (order 624) · Inn(G) = #261 · Out(G) = C₂²×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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 13);