Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#23527 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | C2×#394 |
| prime radical | C2×#575×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,11)(4,15)(5,19)(6,10)(7,13)(8,17)(9,21)(12,26)(14,25)(16,30)(18,24)(20,23)(22,27)(28,31)(29,32)(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)(2,7)(4,16)(5,20)(6,14)(8,22)(9,25)(10,23)(11,19)(12,17)(13,21)(15,28)(18,27)(24,30)(26,29)(31,32);(1,4,5,18,6,17,21,32)(2,8,9,24,10,15,19,29)(3,12,13,27,14,16,20,31)(7,22,11,26,23,28,25,30);(4,17)(8,15)(12,16)(18,32)(22,28)(24,29)(26,30)(27,31)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16515);