Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#23042 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | D42 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2361 |
| prime radical | C73×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ G | |
824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,8,12)(3,13)(4,18,20,5)(6,11,7,24)(9,23)(10,25,22,19)(14,15)(16,29)(17,28)(21,31)(26,32)(27,30)(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);(1,3,7,16,8,17,6,23)(2,9,24,13,12,29,11,28)(4,14,25,31,20,32,19,27)(5,21,10,26,18,30,22,15);(1,4)(2,10)(3,14)(5,11)(6,19)(7,25)(8,20)(9,26)(12,22)(13,30)(15,29)(16,31)(17,32)(18,24)(21,28)(23,27);(1,5,6,22,8,18,7,10)(2,4,11,19,12,20,24,25)(3,15,16,21,17,26,23,30)(9,27,13,14,29,31,28,32)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16030);