Finite Group DatabasebetaFinite Group Databasebeta| order | 26598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D13299 |
| unambiguous semidirect product | C3⋊D4433 |
| unambiguous semidirect product | C11⋊D1209 |
| unambiguous semidirect product | C13⋊D1023 |
| unambiguous semidirect product | C31⋊D429 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C13×C31 | C2 |
| LCS | G ▷ C3×C11×C13×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 13299 |
A minimal faithful permutation representation — 2 generators on 58 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(2,3)(5,14)(6,13)(7,12)(8,11)(9,10)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,58)(30,57)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)Polycyclic presentation:
2,3,11,13,31|b^a=b^2,c^a=c^10,d^a=d^12,e^a=e^306651 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D13299 |
| maximal normal subgroup of | C2×D13299 |
| maximal quotient of | Dic13299, C2×D13299 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26598, 20);