C₇×C₄⋊(C₃⋊C₈) #10620602

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

Aliases

direct product	C₇×C₄⋊(C₃⋊C₈)
unambiguous semidirect product	C₄⋊(C₇×C₃⋊C₈)

Hall	C₃×C₇ ⋊ C₄⋊C₈
Sylow	C₃ ⋊ C₇×C₄⋊C₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 672

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 184);