Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#22889 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | C22×D4 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C22×C73 | C2×C4×D4 |
| prime radical | C73×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C2×C22⋊C8×C73 ◁ G | |
1020 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)(3,4)(5,6,10,14,11,15,9,23)(7,16,18,12,19,27,24,28)(8,13,22,32,21,30,25,31)(17,29,20,26,33,36,34,35)(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);(5,7,10,18,11,19,9,24)(6,12,14,27,15,28,23,16)(8,20,22,33,21,34,25,17)(13,29,32,26,30,36,31,35);(2,4)(8,21)(13,30)(17,33)(20,34)(22,25)(26,35)(29,36)(31,32);(5,8)(6,13)(7,17)(9,25)(10,22)(11,21)(12,26)(14,32)(15,30)(16,29)(18,20)(19,33)(23,31)(24,34)(27,36)(28,35)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 15877);