Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#24475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
1324 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,6,13,8,14,7,12)(3,15,19,28,20,30,18,9)(4,21,24,11,5,25,23,10)(16,26,22,29,31,32,17,27)(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)(2,9)(4,22)(5,17)(6,19)(7,18)(8,20)(10,29)(11,27)(12,30)(13,15)(14,28)(16,23)(21,32)(24,31)(25,26);(1,4,8,5)(2,10,14,11)(3,16,20,31)(6,23,7,24)(9,26,28,32)(12,21,13,25)(15,27,30,29)(17,18,22,19);(1,5,8,4)(2,11,14,10)(3,17,20,22)(6,23,7,24)(9,27,28,29)(12,21,13,25)(15,26,30,32)(16,18,31,19)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17463);