order	176
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×C₅×AGL(1,ℤ/8) (order 320) · Inn(G) = D₄ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

C₁₁×D₈

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₁₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ G

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);(13,19)(14,18)(15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 24);