C₂×ΓL(1,𝔽₈)×D₁₆ #13055036

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×ΓL(1,𝔽₈)×D₁₆
unambiguous semidirect product	(C₂×C₇×D₁₆)⋊C₃

Fitting, Hall	C₂×C₇×D₁₆ ⋊ C₃
Sylow	C₇ ⋊ C₂×C₃×D₁₆

196 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 25 points:

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

maximal subgroup of	ΓL(1,𝔽₈)×#2177, C₂×D₁₆×AGL(1,𝔽₇), #72276641
maximal normal subgroup of	ΓL(1,𝔽₈)×#2177, C₂×D₁₆×AGL(1,𝔽₇), #72276641

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4325);