Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#33495 |
| 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 | #532×C73 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C73 ◁ G | |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,18,14,19,25,33,12,17,23,31,24,32,36,40)(11,16,21,29,22,30,35,39,20,15,26,27,34,28,37,38)(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)(10,15)(12,20)(13,21)(14,22)(16,17)(18,27)(19,28)(23,26)(24,34)(25,35)(29,31)(30,32)(33,38)(36,37)(39,40);(3,8)(5,7)(9,11)(10,16)(12,20)(13,21)(14,22)(15,17)(18,29)(19,30)(23,26)(24,34)(25,35)(27,31)(28,32)(33,39)(36,37)(38,40);(2,6)(5,7)(10,17)(11,20)(18,31)(19,32)(21,26)(22,34)(33,40)(35,37)6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26483);