Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#23674 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C22×C73 | C2×#121 |
| prime radical | C24×C73 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C23×C4×C73 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2)(3,8)(4,6)(5,7)(9,10,13,18,15,20,14,19)(11,16,22,31,23,32,29,36)(12,24,27,35,28,34,26,17)(21,33,25,39,38,40,37,30)(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);(1,3,5,4)(2,6,7,8)(9,11)(10,16)(12,25)(13,22)(14,29)(15,23)(17,33)(18,31)(19,36)(20,32)(21,26)(24,39)(27,38)(28,37)(30,34)(35,40);(1,4,5,3)(2,6,7,8)(9,12)(10,17)(11,21)(13,26)(14,27)(15,28)(16,30)(18,34)(19,24)(20,35)(22,37)(23,38)(25,29)(31,40)(32,39)(33,36);(9,13,15,14)(10,18,20,19)(11,22,23,29)(12,26,28,27)(16,31,32,36)(17,34,35,24)(21,37,38,25)(30,40,39,33)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16662);