Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#32870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#2018 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
502 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,5,9,7,12,6,11)(3,13,16,8,17,23,14,24)(4,10,20,25,21,26,19,27)(15,28,30,22,18,31,29,32)(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);(1,3,5,16,7,17,6,14)(2,8,11,13,12,24,9,23)(4,18,19,30,21,15,20,29)(10,22,25,31,26,32,27,28);(2,9)(3,14)(4,19)(5,6)(10,26)(11,12)(13,23)(15,18)(16,17)(20,21)(22,31)(28,32);(1,4)(2,10)(3,15)(5,20)(6,19)(7,21)(8,22)(9,25)(11,27)(12,26)(13,28)(14,29)(16,30)(17,18)(23,31)(24,32)2044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 25858);