C₇×#4033 #11765131

order	1120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇ · Schur multiplier (H₂) = C₂²

Aliases

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

140 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)(8,9,11,12,10)(13,15,16,14)(19,23)(21,24);(17,19,20,23)(18,21,22,24);(9,10)(11,12)(13,14,16,15)(17,18,20,22)(19,21,23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 737);