Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C210 |
| direct product | C73×#60390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×#41×C73 ◁ G | |
4698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 5 generators on 105 points:
(2,7)(5,16)(8,21)(9,20)(10,17)(12,18)(15,27)(19,23)(22,31)(24,28)(26,29)(30,32)(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);(1,2)(3,8)(4,9)(5,17)(6,10)(7,16)(11,22)(12,19)(13,23)(14,24)(15,28)(18,21)(20,27)(25,32)(26,30)(29,31);(1,3,6,13)(2,8,10,23)(4,11,14,25)(5,18,16,12)(7,19,17,21)(9,22,24,32)(15,29,27,26)(20,30,28,31);(1,4)(2,9)(3,11)(5,15)(6,14)(7,20)(8,22)(10,24)(12,26)(13,25)(16,27)(17,28)(18,29)(19,30)(21,31)(23,32);(4,14)(9,24)(11,25)(15,27)(20,28)(22,32)(26,29)(30,31)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53378);