Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#9105 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #386 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C2×#127×C73 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2,5,7,4,3,6,8)(9,10)(11,17)(12,20,22,15)(13,19)(14,16)(18,21,24,23)(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);(1,3,5,8,4,2,6,7)(9,11,17,10,14,19,13,16)(12,18,21,15,22,24,23,20);(2,3)(7,8)(9,12)(10,15)(11,18)(13,23)(14,22)(16,20)(17,21)(19,24)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 2093);