Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#23345 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| commutator | C23 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C23×C73 | C23×C4 |
| prime radical | C24×C73 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,5)(3,7)(9,10)(11,13)(12,14)(15,16)(17,18,21,24,20,23,28,31)(19,25,27,32,26,22,29,30)(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);(1,2,4,5)(3,8,7,6)(9,11)(10,13)(12,15)(14,16);(2,5)(6,8)(10,14)(11,15)(17,19)(18,22)(20,26)(21,27)(23,25)(24,30)(28,29)(31,32);(1,3,4,7)(2,6,5,8)(10,14)(13,16)(19,26)(22,25)(27,29)(30,32)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16333);