C₅²×#627 #14268276

order	1800
isoclinism	isoclinic class of #625
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₅

Aliases

Hall	C₃²×C₅² ⋊ Q₈
Sylow	C₃² ⋊ C₅²×Q₈

216 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 2 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 470);