C₇×C₄⋊(C₃⋊Dic₃) #11759296

order	1008
isoclinism	isoclinic class of #634
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₇×C₄⋊(C₃⋊Dic₃)
unambiguous semidirect product	C₄⋊(C₇×C₃⋊Dic₃)

Hall	C₃²×C₇ ⋊ C₄⋊C₄
Sylow	C₃² ⋊ C₇×C₄⋊C₄

156 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1008

A minimal faithful permutation representation — 3 generators on 21 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 467);