Finite Group DatabasebetaFinite Group Databasebeta| order | 104 |
| isoclinism | isoclinic class of D13 |
| automorphism | Aut(G) = C22×AGL(1,𝔽13) (order 624) · Inn(G) = D13 · Out(G) = C23×C3 |
| holomorph | G ⋊ Aut(G) = #72259662 |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C13 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D13 |
| commutator, hypocenter | C13 | C8 |
| Fitting, cosocle | C4×C13 | C2 |
| socle, prime radical | C2×C13 | C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C4 | |
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)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,18,17,19,20,21);(1,2,4,6,8,10,12,13,11,9,7,5,3)Polycyclic presentation:
2^3,13|a^2=b,b^2=c,d^a=d^1232 conjugacy classes — view the full character table.
| maximal subgroup of | #6092, C8×D13, #6094, … |
| maximal normal subgroup of | #6092, C8×D13, #6094, … |
| maximal quotient of | #6090, C2×#1055, C3×#1055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(104, 1);