C₇×#6038 #13063783

order	1400
isoclinism	isoclinic class of #6037
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₅²×C₇ ⋊ D₄
Sylow	C₅² ⋊ C₇×D₄

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 140

A minimal faithful permutation representation — 2 generators on 21 points:

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

maximal subgroup of	C₇×#87886, D₇×#6038, #72243103, …
maximal normal subgroup of	C₇×#87886, D₇×#6038, #72243103, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 72);