Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#23365 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| commutator | C23 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle, prime radical | C23×C73 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ G | |
636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,14,12,15,11,16)(17,18)(19,26)(20,24)(21,30)(22,25)(23,29)(27,32)(28,31)(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);(3,8)(5,7)(17,19,22,29)(18,23,25,26)(20,28,21,27)(24,32,30,31);(1,3,4,8)(2,5,6,7)(9,11,12,13)(10,14,15,16)(17,20,22,21)(18,24,25,30)(19,27,29,28)(23,31,26,32);(2,6)(5,7)(17,21,22,20)(18,24,25,30)(19,28,29,27)(23,31,26,32)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16353);