Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C210 |
| direct product | C2×C73×#3011 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| prime radical | C22×2−1+4×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C22×#41×C73 ◁ G | |
4718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 5 generators on 111 points:
(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(3,4)(5,6)(7,8,12,16)(9,17,20,30)(10,14,21,28)(11,23,25,15)(13,24,27,19)(18,31,32,38)(22,35,34,29)(26,36,37,33);(7,9,12,20)(8,13,16,27)(10,18,21,32)(11,24,25,19)(14,26,28,37)(15,30,23,17)(22,36,34,33)(29,38,35,31);(4,6)(7,10)(8,14)(9,18)(11,22)(12,21)(13,26)(15,29)(16,28)(17,31)(19,33)(20,32)(23,35)(24,36)(25,34)(27,37)(30,38);(10,21)(14,28)(18,32)(22,34)(26,37)(29,35)(31,38)(33,36)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53351);