Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#24000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,7)(4,14)(5,18)(6,10)(8,17)(9,20)(11,26)(12,28)(13,23)(15,31)(16,25)(19,24)(21,27)(22,30)(29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,6,13)(2,7,10,23)(4,15)(5,12,20,30)(8,21)(9,22,18,28)(11,16)(14,26)(17,29)(19,27)(24,32)(25,31);(1,4)(2,8)(3,11)(5,19)(6,16)(7,21)(9,25)(10,24)(12,29)(13,15)(14,18)(17,20)(22,31)(23,32)(26,28)(27,30);(5,20)(9,18)(12,30)(14,25)(17,19)(22,28)(26,31)(27,29)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16988);