Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#22895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#454×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(1,2,4,3)(5,6,11,16)(7,17,20,33)(8,13,24,32)(9,15,10,14)(12,25,28,19)(18,35,22,29)(21,30,36,27)(23,34,26,31)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(1,3,4,2)(5,7)(6,12)(8,21)(9,25)(10,19)(11,20)(13,29)(14,33)(15,17)(16,28)(18,23)(22,26)(24,36)(27,31)(30,34)(32,35);(5,7)(6,12)(8,22)(9,19)(10,25)(11,20)(13,30)(14,17)(15,33)(16,28)(18,24)(21,26)(23,36)(27,32)(29,34)(31,35);(5,8)(6,13)(7,18)(9,26)(10,23)(11,24)(12,27)(14,34)(15,31)(16,32)(17,35)(19,36)(20,22)(21,25)(28,30)(29,33)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 15883);