C₃×C₉×C₇⋊C₈ #13094167

order	1512
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₈×C₉ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₉×C₇⋊C₈

derived, Sylow	C₇ ⋊ C₃×C₈×C₉
Hall	C₃×C₇×C₉ ⋊ C₈

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1512

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3)(14,15)(16,17)(18,19)(20,21,22,24,23,25,26,27);(4,5,6,7,8,9,10,11,12)(13,14,16,18,19,17,15)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 64);