C₇×#4099 #11765197

order	1120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂⁴

Aliases

260 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 280

A minimal faithful permutation representation — 3 generators on 20 points:

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

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

maximal subgroup of	ΓL(1,𝔽₈)×#4099, C₇×D₅×#120, D₇×#4099, …
maximal normal subgroup of	ΓL(1,𝔽₈)×#4099, C₇×D₅×#120, D₇×#4099, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 803);