Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C28 |
| direct product | C73×#62619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #529×C73 ◁ G | |
1702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 5 generators on 105 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,12)(11,16)(13,15)(17,18,23,26)(19,24,30,32)(20,21,25,22)(27,28,31,29)(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);(1,3)(2,7)(4,11)(5,13)(6,12)(8,15)(9,10)(14,16)(17,19,23,30)(18,24,26,32)(20,27,25,31)(21,28,22,29);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,22,18,23,25,21,26)(19,27,29,24,30,31,28,32);(3,12)(7,10)(11,13)(15,16)(17,21,23,22)(18,25,26,20)(19,28,30,29)(24,31,32,27);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(17,21,23,22)(18,25,26,20)(19,29,30,28)(24,27,32,31)3577 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 55607);