Finite Group DatabasebetaFinite Group Databasebeta| order | 104 |
| isoclinism | isoclinic class of #261 |
| automorphism | Aut(G) = C2×AGL(1,𝔽13) (order 312) · Inn(G) = #261 · Out(G) = C2×C3 |
| holomorph | G ⋊ Aut(G) = #72229302 |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C13 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #261 |
| commutator, hypocenter | C13 | C8 |
| Fitting, socle, prime radical | C2×C13 | C4 |
| cosocle | Dic13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 2 generators on 21 points:
(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,16,18,17,19,20,21);(1,2,5,8,12,6,10,11,3,7,13,9,4)Polycyclic presentation:
2^3,13|a^2=b,b^2=c,d^a=d^8,d^b=d^1214 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C8, #6118, C2×#1057, … |
| maximal normal subgroup of | D13⋊C8, #6118, C2×#1057, … |
| maximal quotient of | #6092, C2×#1057, C3×#1057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(104, 3);