C₈×C₉×C₁₇ #11927431

order	1224
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₁₆ (order 384) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₂₄
abelian	C₈×C₉×C₁₇

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1224

A minimal faithful permutation representation — 1 generator on 34 points:

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

1224 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1224, 4);