Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#60469 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| socle | C2×C73 | C22×#121 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
2628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 5 generators on 105 points:
(1,2)(3,13)(4,18)(5,10)(6,11)(7,12)(8,16)(9,19)(14,28)(15,24)(17,23)(20,25)(21,26)(22,29)(27,30)(31,32)(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);(1,3,5,16,7,15,6,17)(2,8,11,13,12,23,10,24)(4,14,19,30,20,29,21,31)(9,22,18,27,26,28,25,32);(1,4)(2,9)(3,14)(5,19)(6,21)(7,20)(8,22)(10,25)(11,18)(12,26)(13,27)(15,29)(16,30)(17,31)(23,28)(24,32);(3,15)(8,23)(13,24)(14,29)(16,17)(22,28)(27,32)(30,31);(1,5,7,6)(2,10,12,11)(3,16,15,17)(4,19,20,21)(8,24,23,13)(9,25,26,18)(14,30,29,31)(22,32,28,27)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53457);