C₄⋊(C₇⋊C₁₆) #89257

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₄⋊(C₇⋊C₁₆)

C₇ ⋊ C₄⋊C₁₆

50 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,4,6,7,5,3)(8,9,10,11);(2,3)(4,5)(6,7)(9,11)(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27)

Polycyclic presentation:

2^6,7|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bd,g^a=g^6

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 19);