Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#20860 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#120 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | C2×#385 |
| prime radical | C22×#41×C73 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
1296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,6,11,7,10,5,18)(3,12,14,8,15,23,19,22)(4,9,16,26,17,24,20,25)(13,28,31,32,30,27,29,21)(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);(1,3,6,14,7,15,5,19)(2,8,11,23,10,22,18,12)(4,13,16,31,17,30,20,29)(9,21,26,28,24,32,25,27);(1,4)(2,9)(3,13)(5,20)(6,16)(7,17)(8,21)(10,24)(11,26)(12,27)(14,31)(15,30)(18,25)(19,29)(22,32)(23,28);(2,10)(8,22)(9,24)(11,18)(12,23)(21,32)(25,26)(27,28)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13848);