C₂×C₄×#11717363 #72226401

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

Fitting	C₂×C₄²×C₅² ⋊ C₂×C₄
Sylow	C₅² ⋊ C₂×C₄²×D₄

12660 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 5 generators on 20 points:

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

304 conjugacy classes. The character table is too large to display.

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((7,9,10,8)(11,12,15,13,14)(16,17,20,19,18), (3,4,5,6)(7,8,10,9), (12,13,14,15)(17,19,18,20), (1,2), (8,9)(17,18)(19,20));