C₅×#6432 #11765027

order	1120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₇ ⋊ C₄⋊Q₈
Sylow	C₇ ⋊ C₅×C₄⋊Q₈

136 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 633);