C₃²×(C₂×D₇)⋊C₄ #11759249

order	1008
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂²×C₃

Aliases

204 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 504

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

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

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

maximal subgroup of	C₃²×D₇×C₂²⋊C₄, C₃⋊D₃×(C₂×D₇)⋊C₄, #72246732, …
maximal normal subgroup of	C₃²×D₇×C₂²⋊C₄, C₃⋊D₃×(C₂×D₇)⋊C₄, #72246732, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 420);