Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#60470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C22×#121 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×#41×C73 ◁ G | |
2604 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)(3,11)(5,17)(9,19)(10,20)(12,25)(13,14)(16,28)(18,22)(24,30)(26,27)(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);(1,2,5,7,6,10,17,20)(3,8,13,18,14,23,11,22)(4,9,16,19,15,24,28,30)(12,21,27,29,26,31,25,32);(1,3)(2,8)(4,12)(5,13)(6,14)(7,18)(9,21)(10,23)(11,17)(15,26)(16,27)(19,29)(20,22)(24,31)(25,28)(30,32);(1,4)(2,9)(3,12)(5,16)(6,15)(7,19)(8,21)(10,24)(11,25)(13,27)(14,26)(17,28)(18,29)(20,30)(22,32)(23,31);(4,15)(9,24)(12,26)(16,28)(19,30)(21,31)(25,27)(29,32)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53458);