C₇²×C₃⋊C₈ #11924155

order	1176
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₇²×C₈ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇²×C₃⋊C₈
unambiguous semidirect product	C₃⋊(C₇²×C₈)

derived, Sylow	C₃ ⋊ C₇²×C₈
Hall	C₃×C₇² ⋊ C₈

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1176

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 70);