C₂²×D₄×C₁₃⋊C₃ #11929247

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂²×D₄×C₁₃⋊C₃
unambiguous semidirect product	C₄⋊(C₂³×C₁₃⋊C₃)

Fitting, Hall	C₂²×D₄×C₁₃ ⋊ C₃
Sylow	C₁₃ ⋊ C₂²×C₃×D₄

472 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 4 generators on 21 points:

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

maximal subgroup of	C₂²×D₄×D₁₃⋊C₃, C₂×#88251⋊C₃, C₂×H(5,𝔽₂)×C₁₃⋊C₃
maximal normal subgroup of	C₂²×D₄×D₁₃⋊C₃, C₂×#88251⋊C₃, C₂×H(5,𝔽₂)×C₁₃⋊C₃

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1359);