Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#23525 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #394 |
| 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 | |
1332 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)(3,13)(4,18)(5,10)(6,11)(7,12)(8,16)(9,21)(14,25)(15,24)(17,28)(19,23)(20,27)(22,26)(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)(2,8)(4,19)(5,15)(6,16)(7,17)(9,25)(10,13)(11,28)(12,24)(14,22)(18,32)(20,31)(21,30)(23,27)(26,29);(1,4,5,20,7,22,6,21)(2,9,11,26,12,27,10,18)(3,14,16,31,17,19,15,30)(8,23,13,29,24,25,28,32);(1,5,7,6)(2,10,12,11)(3,15,17,16)(4,20,22,21)(8,13,24,28)(9,18,27,26)(14,30,19,31)(23,29,25,32)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16513);