Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#7886 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C73 | C2×D4 |
| commutator | C2×C4 | C2×C42×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| socle | C22×C73 | C2×#95 |
| prime radical | C24×C73 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C73 ◁ C22×C42×C73 ◁ G | |
550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2)(3,9)(4,12)(5,8)(6,11)(7,13)(10,15)(14,16)(17,18,20,25,22,24,21,26)(19,23,27,31,29,30,28,32)(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)(2,6,8,14)(4,11)(5,10)(7,9,12,15)(13,16)(17,19,21,28,22,29,20,27)(18,23,26,32,24,30,25,31);(3,10)(6,14)(9,15)(11,16)(18,24)(23,30)(25,26)(31,32)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 874);