C₂³×C₇⋊C₂₇ #13094193

order	1512
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₇ · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₇⋊C₂₇

derived, Sylow	C₇ ⋊ C₂³×C₂₇
Hall	C₂³×C₇ ⋊ C₂₇

128 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1512

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2)(8,9,10)(11,13,12)(14,15,18,16,19,24,21,26,31,17,20,25,22,27,32,29,34,37,23,28,33,30,35,38,36,39,40);(3,4)(7,8,9,11,10,12,13);(5,6)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 90);