C₂₇×C₇⋊C₈ #13094107

order	1512
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₈×C₂₇ · Schur multiplier (H₂) = C₁

Aliases

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

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:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 4);