D₂₄ #205

order	48
isoclinism	isoclinic class of #204
automorphism	Aut(G) = D₃×AGL(1,ℤ/8) (order 192) · Inn(G) = D₁₂ · Out(G) = C₂³
holomorph	G ⋊ Aut(G) = #72219802
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₂₄

Fitting	C₃×C₈ ⋊ C₂
Sylow	C₃ ⋊ D₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 11 points:

(1,2,3,4,5,6,7,8)(9,10,11);(2,8)(3,7)(4,6)(10,11)

Polycyclic presentation:

2^4,3|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 7);