C₇×#6180 #13094179

order	1512
isoclinism	isoclinic class of #272
automorphism	?
homology	Abelianization (H₁) = C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	H(3,𝔽₃) ⋊ C₇×C₈
Hall	C₇×H(3,𝔽₃) ⋊ C₈

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 76);