C₂₅×#625 #14267888

order	1800
isoclinism	isoclinic class of #625
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃²×C₂₅ ⋊ D₄
Sylow	C₃² ⋊ D₄×C₂₅

105 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(27,29)(31,32)(33,34,35);(26,27)(28,29)(30,31,32)(34,35)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 82);