C₁₇×C₉⋊C₈ #11927428

order	1224
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₈×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₉⋊C₈
unambiguous semidirect product	C₉⋊(C₈×C₁₇)

derived, Sylow	C₉ ⋊ C₈×C₁₇
Hall	C₉×C₁₇ ⋊ C₈

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1224

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)(19,21)(20,24)(22,23)(25,26)(27,28,29,31,30,32,33,34);(18,26,21,24,23,22,20,19,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1224, 1);