order	88
isoclinism	isoclinic class of Dic₂₂
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₁) (order 440) · Inn(G) = C₂×D₁₁ · Out(G) = C₂×C₅
holomorph	G ⋊ Aut(G) = #72222682
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

C₂²⋊D₁₁

Splittings

Fitting	C₂²×C₁₁ ⋊ C₂
Sylow	C₁₁ ⋊ D₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 44

A minimal faithful permutation representation — 2 generators on 15 points:

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

Polycyclic presentation:

2^3,11|b^a=bc,d^a=d^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(88, 7);