C₅×#6391 #11764487

order	1120
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₅×C₇ ⋊ #106
Sylow	C₇ ⋊ C₅×#106

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1120

A minimal faithful permutation representation — 2 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 93);