Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33541 |
| 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 | |
1104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,8)(3,13)(4,6)(5,16)(9,24)(10,17)(11,22)(12,23)(14,29)(15,20)(18,19)(21,25)(26,32)(27,30)(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)(3,9)(4,10)(5,17)(6,11)(7,12)(8,16)(13,25)(14,30)(15,27)(18,23)(19,22)(20,26)(21,28)(24,29)(31,32);(1,3)(2,9)(4,13)(5,14)(6,20)(7,15)(8,21)(10,25)(11,26)(12,27)(16,28)(17,30)(18,31)(19,29)(22,24)(23,32);(1,4,7,6)(2,10,12,11)(3,13,15,20)(5,16,19,18)(8,22,23,17)(9,25,27,26)(14,28,29,31)(21,24,32,30)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26529);