Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#23999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
1146 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)(4,8)(5,18)(6,10)(7,15)(9,21)(12,19)(13,29)(14,25)(16,26)(17,24)(20,23)(22,31)(27,30)(28,32)(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)(3,12,14,7)(4,8)(5,9)(6,10)(11,15,25,19)(13,28,30,22)(16,23)(17,24)(18,21)(20,26)(27,32,29,31);(1,3)(2,7)(4,13)(5,19)(6,14)(8,22)(9,25)(10,12)(11,18)(15,21)(16,32)(17,30)(20,31)(23,27)(24,28)(26,29);(1,4,6,17)(2,8,10,24)(3,13,14,30)(5,20,21,16)(7,22,12,28)(9,26,18,23)(11,27,25,29)(15,32,19,31)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16987);