Finite Group DatabasebetaFinite Group Databasebeta| order | 208 |
| automorphism | Aut(G) = C2×D4×AGL(1,𝔽13) (order 2496) · Inn(G) = C22×D13 · Out(G) = C23×C3 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D13 |
| commutator, socle, cosocle | C2×C13 | C23 |
| Fitting | D4×C13 | C2 |
| hypercenter | D4 | D13 |
| hypocenter | C13 | #41 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,19)(16,20);(14,16,17,20)(15,18,19,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,18)(17,19)(20,21)Polycyclic presentation:
2^4,13|b^2=d,c^a=cd,e^a=e^12,c^b=cd40 conjugacy classes — view the full character table.
| maximal subgroup of | #88116, #88165, #88166, … |
| maximal normal subgroup of | #88116, #88165, #88166, … |
| maximal quotient of | #88131, #88132, #88133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(208, 40);