D₈₈ #4315

order	176
isoclinism	isoclinic class of #4314
automorphism	Aut(G) = AGL(1,ℤ/8)×AGL(1,𝔽₁₁) (order 3520) · Inn(G) = D₄₄ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₈₈

Fitting	C₈×C₁₁ ⋊ C₂
Sylow	C₁₁ ⋊ D₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 2 generators on 19 points:

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

Polycyclic presentation:

2^4,11|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 6);