Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#11712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C24×C73 | SD16 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ C23×C8×C73 ◁ G | |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 113 points:
(1,2)(3,7,8,5)(4,6)(9,10,12,17,15,20,14,19)(11,21,22,35,25,38,24,37)(13,27,26,18,30,34,29,36)(16,28,31,23,33,39,32,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(1,3)(2,5)(4,8)(6,7)(9,11,15,25)(10,16,20,33)(12,24,14,22)(13,28,30,39)(17,32,19,31)(18,35,36,37)(21,27,38,34)(23,26,40,29);(9,12,15,14)(10,17,20,19)(11,22,25,24)(13,26,30,29)(16,31,33,32)(18,34,36,27)(21,35,38,37)(23,39,40,28)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 4700);