Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C27 |
| direct product | C73×#20939 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#120 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | C2×#386 |
| prime radical | C2×#575×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G | |
1668 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)(3,12,15,24)(4,16)(5,11)(6,20)(7,10)(8,14,23,19)(9,17)(13,28,31,22)(18,26)(21,25)(27,29,32,30)(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);(1,3,5,19,7,15,6,14)(2,8,11,24,10,23,20,12)(4,13,17,30,18,31,21,29)(9,22,26,32,25,28,16,27);(1,4)(2,9)(3,13)(5,17)(6,21)(7,18)(8,22)(10,25)(11,26)(12,27)(14,29)(15,31)(16,20)(19,30)(23,28)(24,32);(2,10)(8,23)(9,25)(11,20)(12,24)(16,26)(22,28)(27,32)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13927);