Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of D13 |
| automorphism | Aut(G) = C2×C4×AGL(1,𝔽13) (order 1248) · Inn(G) = D13 · Out(G) = C22×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 | C8 | D13 |
| commutator, hypocenter | C13 | C16 |
| Fitting, cosocle | C8×C13 | C2 |
| socle, prime radical | C2×C13 | C8 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C8 | |
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)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,19,17,20,22,25,18,21,23,26,24,27,28,29);(1,2,4,6,8,10,12,13,11,9,7,5,3)Polycyclic presentation:
2^4,13|a^2=b,b^2=c,c^2=d,e^a=e^1264 conjugacy classes — view the full character table.
| maximal subgroup of | #88036, C16×D13, #88038, … |
| maximal normal subgroup of | #88036, C16×D13, #88038, … |
| maximal quotient of | #88034, C2×#6090, C3×#6090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 1);