Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#20294 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#1624 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,6)(4,12)(7,13)(8,15)(9,16)(10,14)(17,18)(19,22)(20,23)(21,24)(25,28)(26,30)(27,31)(29,32)(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)(3,9)(4,13)(5,7)(6,12)(8,10)(11,15)(14,16)(17,19)(18,22)(20,27)(21,26)(23,31)(24,30)(25,29)(28,32);(2,7)(6,13)(8,16)(9,15)(18,23)(19,26)(20,28)(22,29)(24,25)(30,31);(1,3,5,11)(2,8,7,16)(4,14,12,10)(6,15,13,9)(18,24)(22,30)(23,25)(29,31)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13282);