A₅×#10597244 #49137838

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

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 275

A minimal faithful permutation representation — 2 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 974);