Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | Aut(G) = C23×AGL(1,𝔽13) (order 1248) · Inn(G) = C2×D13 · Out(G) = C2×C3×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C13 ⋊ C2 |
| Sylow | C13 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D13 |
| commutator, socle | C2×C13 | C2×C4 |
| Fitting | C8×C13 | C2 |
| prime radical | C2×D13 | C4 |
| cosocle | C4×C13 | C22 |
| hypercenter | C8 | D13 |
| hypocenter | C13 | M16 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16,19,17,18,20,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,18)(19,21)Polycyclic presentation:
2^4,13|b^2=c,c^2=d,b^a=bd,e^a=e^1258 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#6094, #88155, M16×D13, … |
| maximal normal subgroup of | C2×#6094, #88155, M16×D13, … |
| maximal quotient of | #88054, #88055, #88060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 5);