Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C210 |
| direct product | C2×C73×#3022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| prime radical | C2×#585×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
4742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(3,4,9,14)(5,15,18,27)(6,11,20,26)(7,13,8,12)(10,21,24,17)(16,30,33,29)(19,28,22,25)(23,31,34,32);(3,5)(4,10)(6,16)(7,17)(8,21)(9,18)(11,23)(12,15)(13,27)(14,24)(19,31)(20,33)(22,32)(25,29)(26,34)(28,30);(3,6)(4,11)(5,16)(7,19)(8,22)(9,20)(10,23)(12,25)(13,28)(14,26)(15,29)(17,31)(18,33)(21,32)(24,34)(27,30);(3,7,9,8)(4,12,14,13)(5,17,18,21)(6,19,20,22)(10,15,24,27)(11,25,26,28)(16,31,33,32)(23,29,34,30)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53374);