Finite Group DatabasebetaFinite Group Databasebeta| order | 26026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C11⋊((C13⋊D13)⋊C7) |
| unambiguous semidirect product | (C11⋊(C13⋊D13))⋊C7 |
| Fitting, socle, derived, Hall | C11×C132 ⋊ C2×C7 |
| Hall | C11×C132⋊C7 ⋊ C2 |
| Hall | C11⋊(C13⋊D13) ⋊ C7 |
| Hall | C132⋊C7 ⋊ D11 |
| Sylow | C132 ⋊ C7×D11 |
| Sylow | C11 ⋊ (C13⋊D13)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C132 | C2×C7 |
| LCS | G ▷ C11×C132 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 102 |
| transitive degree | μt(G) = 1001 |
A minimal faithful permutation representation — 2 generators on 102 points:
(1,2,4,9,20,40,57)(3,14,15,22,42,69,73,6,7,30,31,46,63,85)(5,25,28,62,58,74,86,12,13,50,51,75,76,72)(8,34,35,47,64,84,87,17,18,29,49,70,82,91)(10,48,41,79,80,37,38,23,24,60,61,89,19,54)(11,43,44,59,83,55,53,26,21,65,66,77,39,36)(16,32,45,67,81,90,71,33,27,52,68,78,88,56)(93,94)(95,96)(97,98)(99,100)(101,102);(1,3,8,19,39,56,72,86,71,55,37,17,6)(2,5,7,16,18,36,38,54,53,34,33,14,12)(4,10,25,26,30,35,32,27,29,15,11,13,23)(9,21,45,22,24,28,47,49,50,48,31,52,43)(20,41,62,65,46,64,67,68,70,42,44,51,60)(40,58,63,81,82,59,61,79,66,84,78,69,75)(57,73,87,80,83,90,74,76,88,77,89,91,85)(92,93,95,97,99,101,102,100,98,96,94)Polycyclic presentation:
2,7,11,13^2|c^a=c^10,d^a=d^12,e^a=e^12,d^b=de,e^b=d^6e^7181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26026, 14);