Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C2×C4 |
| direct product | C73×#11750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#102 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | #466×C73 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ C2×C4×C8×C73 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 3 generators on 113 points:
(2,6,7,8)(9,10,13,18,15,20,14,19)(11,21,24,34,22,37,25,38)(12,26,28,17,30,35,29,36)(16,27,32,23,31,40,33,39)(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);(1,2)(3,6)(4,8)(5,7)(9,11)(10,16)(12,27)(13,25)(14,24)(15,22)(17,34)(18,33)(19,32)(20,31)(21,35)(23,29)(26,37)(28,39)(30,40)(36,38);(1,3,5,4)(2,6,7,8)(11,22)(16,31)(21,37)(23,39)(24,25)(27,40)(32,33)(34,38)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 4738);