Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#8500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #379 |
| commutator | C42 | C22×C4×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C73×#3546 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2)(3,10,12,6)(4,9)(5,8)(7,11,15,13)(14,16)(17,18,21,24,22,26,20,25)(19,27,28,23,29,31,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3)(2,6)(4,11)(5,12)(7,9)(8,10)(13,14)(15,16)(17,19)(18,23)(20,30)(21,28)(22,29)(24,31)(25,27)(26,32);(1,3)(2,7)(4,13)(5,12)(6,9)(8,15)(10,16)(11,14)(18,24)(20,21)(23,31)(25,26)(27,32)(28,30)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1488);