Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C73 · Schur multiplier (H2) = C29 |
| direct product | C2×C73×#2932 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| commutator | C22 | C24×C4×C73 |
| Frattini, cosocle | C2×C4 | C25×C73 |
| socle | C23×C73 | C23×C4 |
| prime radical | C2×#532×C73 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ G | |
2806 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 5 generators on 95 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(3,4)(5,6)(7,8,11,15,12,14,20,21)(9,13,17,10,16,18,22,19);(4,6)(7,9)(8,13)(10,15)(11,17)(12,16)(14,18)(19,21)(20,22);(7,10,11,18,12,19,20,13)(8,9,15,17,14,16,21,22);(8,14)(9,16)(15,21)(17,22)6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53124);