C₇×#812 #10620610

order	672
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ M₃₂
Sylow	C₃ ⋊ C₇×M₃₂

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 192);