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) = #72229310 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#261 |
| unambiguous semidirect product | D13⋊C4 |
| Fitting, socle | C2×C13 ⋊ C4 |
| derived, Sylow | C13 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #261 |
| commutator, hypocenter | C13 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13 | C4 |
| prime radical | C2×D13 | C2 |
| cosocle | D13 | C22 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 26 |
A minimal faithful permutation representation — 2 generators on 15 points:
(4,5,6,8)(7,10,11,15)(9,13,14,12);(1,2)(3,4,7,10,14,8,12,13,5,9,15,11,6)14 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#261, C4⋊#261, C22⋊#261, … |
| maximal normal subgroup of | C4×#261, C4⋊#261, C22⋊#261, … |
| maximal quotient of | D13⋊C8, #6118, C4×#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(104, 12);