Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C210 |
| direct product | C73×#60391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×#41×C73 ◁ G | |
4666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 5 generators on 105 points:
(1,2,7,4)(3,11,15,24)(5,9,18,16)(6,17,21,10)(8,20,12,14)(13,25,27,32)(19,29,30,23)(22,31,26,28)(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)(4,12)(5,13)(6,20)(7,15)(9,22)(10,24)(11,17)(14,21)(16,26)(18,27)(19,31)(23,32)(25,29)(28,30);(1,4,7,2)(3,12,15,8)(5,16,18,9)(6,10,21,17)(11,20,24,14)(13,26,27,22)(19,23,30,29)(25,31,32,28);(1,5)(2,9)(3,13)(4,16)(6,19)(7,18)(8,22)(10,23)(11,25)(12,26)(14,28)(15,27)(17,29)(20,31)(21,30)(24,32);(5,18)(9,16)(13,27)(19,30)(22,26)(23,29)(25,32)(28,31)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53379);