Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C2×C4 |
| direct product | C73×#11866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | #466×C73 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 3 generators on 121 points:
(1,2)(3,9,11,6)(4,7)(5,8)(10,15,12,14)(13,16)(17,18,22,28,24,30,23,29)(19,31,34,46,36,47,35,42)(20,37,21,40,39,27,38,26)(25,41,43,33,45,32,44,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(1,3)(2,6)(4,12)(5,11)(7,15)(8,9)(10,13)(14,16)(17,19)(18,25)(20,33)(21,41)(22,35)(23,34)(24,36)(26,31)(27,46)(28,44)(29,43)(30,45)(32,38)(37,42)(39,48)(40,47);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,20,23,38,24,39,22,21)(18,26,28,37,30,40,29,27)(19,32,35,33,36,41,34,48)(25,42,43,31,45,46,44,47)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 4854);