C₃²×C₅×C₁₃×D₁₁ #27166100

order	12870
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₅×C₁₃×D₁₁

	subgroup	G/H
center, hypercenter	C₃²×C₅×C₁₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₃²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃²×C₅×C₁₃

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 6435

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

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

4095 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 95);