Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | Aut(G) = C24×AGL(1,𝔽13) (order 2496) · Inn(G) = C2×D13 · Out(G) = C22×C3×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D13 |
| commutator | C2×C13 | C2×C4 |
| Fitting | C2×C4×C13 | C2 |
| socle, prime radical, cosocle | C22×C13 | C22 |
| hypercenter | C2×C4 | D13 |
| hypocenter | C13 | C4⋊C4 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16,17)(19,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(18,19,20,21)Polycyclic presentation:
2^4,13|a^2=d,b^2=c,b^a=bd,e^a=e^1258 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic26, #88124, #88126, … |
| maximal normal subgroup of | C4×Dic26, #88124, #88126, … |
| maximal quotient of | #88047, #88048, #88054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 12);