Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#22898 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | D42 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2358 |
| prime radical | C73×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,5,11,6,12,21,10)(3,9,15,24,16,23,14,7)(4,17,18,27,20,26,19,8)(13,28,30,32,31,22,29,25)(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);(1,3,5,15,6,16,21,14)(2,7,11,9,12,24,10,23)(4,13,18,30,20,31,19,29)(8,22,17,25,27,28,26,32);(1,4)(2,8)(3,13)(5,18)(6,20)(7,22)(9,25)(10,26)(11,17)(12,27)(14,29)(15,30)(16,31)(19,21)(23,32)(24,28);(1,3)(2,9)(4,13)(5,15)(6,16)(7,10)(8,25)(11,24)(12,23)(14,21)(17,28)(18,30)(19,29)(20,31)(22,26)(27,32)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 15886);