order	176
automorphism	Aut(G) = C₂×S₄×AGL(1,𝔽₁₁) (order 5280) · Inn(G) = C₂²×D₁₁ · Out(G) = C₂×C₅×D₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×D₁₁

Splittings

Fitting	Q₈×C₁₁ ⋊ C₂
Sylow	C₁₁ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 33);