C₂₃×C₂²⋊D₇ #13046239

order	1288
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₃×C₂²⋊D₇
unambiguous semidirect product	C₂²⋊(D₇×C₂₃)

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 644

A minimal faithful permutation representation — 2 generators on 34 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1288, 21);