Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#33485 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C73 | C24 |
| commutator | C22 | C23×C8×C73 |
| Frattini, cosocle | C2×C8 | C24×C73 |
| socle | C22×C73 | C23×C8 |
| prime radical | C2×#41×C73 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C73 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,18,15,11,19,21,13,16,22,23,12,20,17,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,5)(6,8)(10,16)(11,20)(18,23)(21,24);(9,11,14,21,15,16,19,23,13,20,22,24,12,10,17,18);(1,3,4,7)(2,6,5,8)(9,12,13,15)(10,11,16,20)(14,17,22,19)(18,21,23,24)7300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26473);