Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#19792 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,6,4)(3,9,13,16)(5,14,15,8)(7,11,10,12)(17,18,21,25)(19,22,27,31)(20,23,28,24)(26,29,32,30)(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);(1,3)(2,7)(4,10)(5,11)(6,13)(8,16)(9,14)(12,15)(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(1,4,6,2)(3,10,13,7)(5,14,15,8)(9,12,16,11)(18,23)(20,28)(22,29)(24,25)(26,32)(30,31);(3,11)(5,15)(7,16)(8,14)(9,10)(12,13)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12780);