Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of #261 |
| automorphism | Aut(G) = S4×AGL(1,𝔽13) (order 3744) · Inn(G) = #261 · Out(G) = C3×S4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#261 |
| unambiguous semidirect product | D13⋊(C2×C4) |
| Fitting, socle | C22×C13 ⋊ C4 |
| derived, Sylow | C13 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #261 |
| commutator, hypocenter | C13 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13 | C4 |
| prime radical | C22×D13 | C2 |
| cosocle | D13 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22 | |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 52 |
A minimal faithful permutation representation — 3 generators on 17 points:
(6,7,8,10)(9,12,13,17)(11,15,16,14);(3,4)(5,6,9,12,16,10,14,15,7,11,17,13,8);(1,2)28 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#261)⋊C4, C2×C4×#261, C2×C4⋊#261, … |
| maximal normal subgroup of | (C2×#261)⋊C4, C2×C4×#261, C2×C4⋊#261, … |
| maximal quotient of | C2×D13⋊C8, C2×#6118, D13⋊M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 49);