Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C28 |
| direct product | C73×#62606 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #529×C73 ◁ G | |
1666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 5 generators on 121 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,12)(11,16)(13,15)(17,18)(19,28)(20,32)(21,26)(22,27)(23,37)(24,31)(25,35)(29,43)(30,40)(33,41)(34,47)(36,39)(38,48)(42,44)(45,46)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(1,3)(2,7)(4,11)(5,13)(6,12)(8,15)(9,10)(14,16)(17,19)(18,24)(20,29)(21,36)(22,31)(23,30)(25,38)(26,40)(27,28)(32,46)(33,48)(34,45)(35,44)(37,39)(41,42)(43,47);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,21,33,22,34,23,35)(18,25,37,47,27,41,26,32)(19,29,36,48,31,45,30,44)(24,38,39,43,28,42,40,46);(3,12)(7,10)(11,13)(15,16)(17,21,22,23)(18,26,27,37)(19,30,31,36)(20,33,34,35)(24,39,28,40)(25,32,41,47)(29,44,45,48)(38,43,42,46);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(18,27)(19,31)(20,34)(26,37)(30,36)(33,35)(38,42)(43,46)3577 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 55594);