C₂²×C₁₁×3₋¹⁺² #11924696

order	1188
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₁×3₋¹⁺²

	subgroup	G/H
center, socle	C₂²×C₃×C₁₁	C₃²
commutator, Frattini, cosocle	C₃	C₂²×C₃²×C₁₁
prime radical	C₂²×C₃²×C₁₁	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₁₁ ◁ G

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 396

A minimal faithful permutation representation — 2 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 66);