C₂⁶×#1043 #72258463

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²¹

Aliases

Fitting, socle	C₂⁶×C₅² ⋊ C₄
derived, Sylow	C₅² ⋊ C₂⁶×C₄

444792 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 7 generators on 22 points:

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

640 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((11,12)(13,14,17,15,16), (9,10)(18,19,22,20,21), (7,8), (5,6), (14,15,16,17)(19,20,21,22), (3,4), (1,2));