C₂²×C₅²⋊C₉ #11744652

order	900
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₅²⋊C₉

derived, Sylow	C₅² ⋊ C₂²×C₉
Hall	C₂²×C₅² ⋊ C₉

50 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2)(5,6,8)(7,10,12)(9,14,17)(11,16,18)(13,19,15)(20,21,23,22,24,26,25,27,28);(3,4)(5,7,11,17,19)(6,10,16,9,15)(8,14,12,13,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(900, 64);