C₃²×#6029 #14268068

order	1800
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₃²×C₈ · Schur multiplier (H₂) = C₃×C₅

Aliases

derived, Sylow	C₅² ⋊ C₃²×C₈
Hall	C₃²×C₅² ⋊ C₈

192 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1800

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 262);