Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of #6118 |
| automorphism | Aut(G) = D4×AGL(1,𝔽13) (order 1248) · Inn(G) = C2×#261 · Out(G) = C22×C3 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C13 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#261 |
| commutator, socle | C2×C13 | C2×C4 |
| Fitting | C4×C13 | C4 |
| prime radical | C2×D13 | C4 |
| cosocle | Dic13 | C22 |
| hypercenter | C4 | #261 |
| hypocenter | C13 | M16 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ 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:
(1,2,5,8,12,6,10,11,3,7,13,9,4)(14,16,18,17)(15,19,20,21);(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,17,19,18,20,16,21)Polycyclic presentation:
2^4,13|a^2=c,b^2=d,c^2=d,b^a=bd,e^a=e^8,e^c=e^1222 conjugacy classes — view the full character table.
| maximal subgroup of | #88103, #88104, #88116, … |
| maximal normal subgroup of | #88103, #88104, #88116, … |
| maximal quotient of | C4⋊#1057, #88110, #88111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 29);