Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C73 · Schur multiplier (H2) = C210 |
| direct product | C73×#60070 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C73 |
| Frattini, cosocle | C23 | C25×C73 |
| socle | C2×C73 | C23×C22⋊C4 |
| prime radical | C2×#585×C73 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×#41×C73 ◁ G | |
4892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 5 generators on 105 points:
(1,2)(3,11,14,7)(4,8)(5,9)(6,10)(12,23,25,18)(13,24,27,19)(15,20)(16,21)(17,22)(26,31,32,29)(28,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3)(2,7)(4,12)(5,13)(6,14)(8,18)(9,19)(10,11)(15,25)(16,26)(17,27)(20,23)(21,29)(22,24)(28,32)(30,31);(1,4)(2,8)(3,12)(5,16)(6,15)(7,18)(9,21)(10,20)(11,23)(13,26)(14,25)(17,28)(19,29)(22,30)(24,31)(27,32);(4,15)(8,20)(12,25)(16,28)(18,23)(21,30)(26,32)(29,31);(1,5,6,17)(2,9,10,22)(3,13,14,27)(4,16,15,28)(7,19,11,24)(8,21,20,30)(12,26,25,32)(18,29,23,31)5986 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53058);