Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of #261 |
| automorphism | Aut(G) = C4×AGL(1,𝔽13) (order 624) · Inn(G) = #261 · Out(G) = C3×C4 |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C13 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #261 |
| commutator, hypocenter | C13 | C16 |
| Fitting | C4×C13 | C4 |
| socle, prime radical | C2×C13 | C8 |
| cosocle | #1055 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 29 points:
(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,16,19,17,20,22,25,18,21,23,26,24,27,28,29);(1,2,5,8,12,6,10,11,3,7,13,9,4)Polycyclic presentation:
2^4,13|a^2=b,b^2=c,c^2=d,e^a=e^8,e^b=e^1228 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C16, #88098, C2×#6092, … |
| maximal normal subgroup of | D13⋊C16, #88098, C2×#6092, … |
| maximal quotient of | #88036, C2×#6092, C3×#6092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 3);