C₂²×C₄²×ΓL(1,𝔽₈) #13060672

order	1344
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

Fitting, Hall	C₂²×C₄²×C₇ ⋊ C₃
derived, Sylow	C₇ ⋊ C₂²×C₃×C₄²

996 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 19 points:

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

maximal subgroup of	ΓL(1,𝔽₈)×#1437, C₂²×ΓL(1,𝔽₈)×#127, C₂²×C₄²×AGL(1,𝔽₇), …
maximal normal subgroup of	ΓL(1,𝔽₈)×#1437, C₂²×ΓL(1,𝔽₈)×#127, C₂²×C₄²×AGL(1,𝔽₇), …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 9961);