Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#60471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C22×#121 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×#41×C73 ◁ G | |
2630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 5 generators on 105 points:
(2,7)(3,12)(5,8)(10,19)(11,20)(13,26)(14,15)(17,21)(18,23)(25,30)(27,28)(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);(1,2,8,20,6,11,5,7)(3,9,12,23,15,24,14,18)(4,10,21,30,16,25,17,19)(13,22,26,32,27,31,28,29);(1,3)(2,9)(4,13)(5,14)(6,15)(7,18)(8,12)(10,22)(11,24)(16,27)(17,28)(19,29)(20,23)(21,26)(25,31)(30,32);(1,4)(2,10)(3,13)(5,17)(6,16)(7,19)(8,21)(9,22)(11,25)(12,26)(14,28)(15,27)(18,29)(20,30)(23,32)(24,31);(4,16)(10,25)(13,27)(17,21)(19,30)(22,31)(26,28)(29,32)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53459);