C₂²×C₃×C₂₃ #63288

order	276
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×D₃×C₁₁ (order 264) · Inn(G) = C₁ · Out(G) = C₂²×D₃×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₂₃
multiplicative	(ℤ/329)ˣ, (ℤ/417)ˣ, (ℤ/423)ˣ, (ℤ/556)ˣ, (ℤ/658)ˣ, (ℤ/834)ˣ, (ℤ/846)ˣ

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 276

A minimal faithful permutation representation — 2 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(276, 10);