Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33531 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,7)(4,14)(5,17)(8,22)(9,21)(10,25)(12,27)(13,26)(15,19)(16,30)(18,31)(20,23)(24,32)(28,29)(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)(3,8)(4,15)(5,19)(6,9)(7,14)(10,17)(11,23)(12,28)(13,29)(16,32)(18,25)(20,30)(21,31)(22,27)(24,26);(1,3)(2,8)(4,16)(5,13)(6,11)(7,20)(9,23)(10,24)(12,18)(14,30)(15,32)(17,26)(19,29)(21,22)(25,28)(27,31);(3,11)(8,23)(12,16)(13,26)(20,22)(24,29)(27,30)(28,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26519);