C₂₃×C₇⋊C₈ #13046219

order	1288
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₈×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×C₇⋊C₈
unambiguous semidirect product	C₇⋊(C₈×C₂₃)

derived, Sylow	C₇ ⋊ C₈×C₂₃
Hall	C₇×C₂₃ ⋊ C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1288

A minimal faithful permutation representation — 2 generators on 38 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1288, 1);