C₇²×#170 #14519951

order	1960
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₇²×C₈ · Schur multiplier (H₂) = C₇

Aliases

derived, Sylow	C₅ ⋊ C₇²×C₈
Hall	C₅×C₇² ⋊ C₈

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5,6,7)(16,17,18,19)(20,21,22,24,23,25,26,27);(8,9,10,11,12,13,14)(15,16,17,19,18)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 48);