C₁₇×#683 #13062692

order	1360
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₅×C₁₇ ⋊ C₄⋊C₄
Sylow	C₅ ⋊ C₄⋊C₄×C₁₇

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1360

A minimal faithful permutation representation — 2 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 60);