A₅×#10597245 #49137839

order	36300
automorphism	?
homology	Abelianization (H₁) = C₅ · Schur multiplier (H₂) = C₂×C₁₁

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 975);