Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#23474 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C73 |
| socle | C2×C73 | C2×#393 |
| prime radical | C22×#41×C73 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,7)(4,14,17,8)(5,9)(6,10)(11,24,15,19)(12,20)(13,21)(16,27,29,22)(18,23)(25,32,28,30)(26,31)(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)(4,15,17,11)(5,12)(6,13)(8,19,14,24)(9,20)(10,21)(16,28,29,25)(18,26)(22,30,27,32)(23,31);(1,4)(2,8)(3,11)(5,16)(6,17)(7,19)(9,22)(10,14)(12,25)(13,15)(18,29)(20,30)(21,24)(23,27)(26,28)(31,32);(1,5,6,18)(2,9,10,23)(3,12,13,26)(4,16,17,29)(7,20,21,31)(8,22,14,27)(11,25,15,28)(19,30,24,32)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16462);