Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#13098 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #1898 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C2×#41 | C23×C73 |
| prime radical | C73×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×C4×C73 ◁ C2×2−1+4×C73 ◁ G | |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2)(3,5,13,20)(4,14,17,26)(6,9)(7,10)(8,16,25,22)(11,28)(12,19,21,30)(15,29)(18,31)(23,27)(24,32)(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);(1,3,5,10,7,13,20,2)(4,11,18,25,17,24,15,8)(6,21,19,9,23,12,30,27)(14,22,29,32,26,16,31,28);(1,4)(2,8)(3,11)(5,18)(6,22)(7,17)(9,26)(10,25)(12,31)(13,24)(14,27)(15,20)(16,23)(19,32)(21,29)(28,30)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6086);