A₅×#10597243 #49137837

order	36300
automorphism	?
homology	Abelianization (H₁) = C₅ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	C₁₁² ⋊ C₅×A₅
socle, derived	C₁₁²×A₅ ⋊ C₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₁₁²×A₅	C₅
Fitting, cosocle	C₁₁²	C₅×A₅
LCS	G ▷ C₁₁²×A₅
UCS	C₁

280 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 605

A minimal faithful permutation representation — 3 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 973);