C₈×C₇⋊C₂₇ #13094105

order	1512
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₈×C₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈×C₇⋊C₂₇
unambiguous semidirect product	(C₇×C₈)⋊C₂₇

derived, Sylow	C₇ ⋊ C₈×C₂₇
Hall	C₇×C₈ ⋊ C₂₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1512

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5,6,7,8)(10,11,12)(13,15,14)(16,17,20,18,21,26,23,28,33,19,22,27,24,29,34,31,36,39,25,30,35,32,37,40,38,41,42);(9,10,11,13,12,14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 2);