C₅×#63225 #13062676

order	1360
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 44);