C₇×#6032 #13063764

order	1400
isoclinism	isoclinic class of #1042
automorphism	?
homology	Abelianization (H₁) = C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅² ⋊ C₇×C₈
Hall	C₅²×C₇ ⋊ C₈

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 280

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5,6,7)(8,9,10,12,11,13,14,15)(17,18)(19,20)(22,23,24,25);(16,17,19,20,18)(21,22,25,23,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 53);