Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | Aut(G) = C2×D4×AGL(1,𝔽13) (order 2496) · Inn(G) = C2×D13 · Out(G) = C22×C3×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C13 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D13 |
| commutator, socle | C2×C13 | C2×C4 |
| Fitting | C2×C4×C13 | C2 |
| prime radical | C22×C13 | C4 |
| cosocle | C4×C13 | C22 |
| hypercenter | C2×C4 | D13 |
| hypocenter | C13 | M16 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
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)(15,18)(19,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,19,17,18,20,21)Polycyclic presentation:
2^4,13|a^2=c,c^2=d,b^a=bd,e^a=e^1258 conjugacy classes — view the full character table.
| maximal subgroup of | #88045, #88059, #88062, … |
| maximal normal subgroup of | #88045, #88059, #88062, … |
| maximal quotient of | #88043, C4⋊#1055, C22⋊#1055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 10);