Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C24×C4 |
| direct product | C73×#17404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C24×C73 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C42×C73 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,11,14,7)(4,8)(5,9)(6,10)(12,16,13,15)(17,18,21,24,22,25,20,29)(19,23,28,31,26,30,27,32)(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);(1,3,6,14)(2,7,10,11)(4,12,5,13)(8,15,9,16)(17,19)(18,23)(20,27)(21,28)(22,26)(24,31)(25,30)(29,32);(1,4,6,5)(2,8,10,9)(3,12,14,13)(7,15,11,16)(19,26)(23,30)(27,28)(31,32);(1,5,6,4)(2,9,10,8)(3,13,14,12)(7,16,11,15)(17,20,22,21)(18,24,25,29)(19,27,26,28)(23,31,30,32)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 10392);