C₅×#6386 #11764483

order	1120
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₅×C₇ ⋊ M₃₂
Sylow	C₇ ⋊ C₅×M₃₂

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 560

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 89);