order	96
automorphism	Aut(G) = D₄×S₄ (order 192) · Inn(G) = C₂²×A₄ · Out(G) = C₂²
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

2₋¹⁺⁴⋊C₃

Splittings

2₋¹⁺⁴ ⋊ C₃

	subgroup	G/H
center, Frattini, socle	C₂	C₂²×A₄
commutator, cosocle, hypocenter	Q₈	C₂²×C₃
Fitting	2₋¹⁺⁴	C₃
hypercenter	D₄	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂ ◁ D₄

46 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 16

A minimal faithful permutation representation — 2 generators on 16 points:

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

Polycyclic presentation:

2^2,3,2^3|d^2=f,e^2=f,b^a=bf,d^c=e,e^c=de,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 202);