Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#23530 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C22×C73 | C2×#121 |
| prime radical | C2×#575×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C23×C4×C73 ◁ G | |
1350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(1,2)(3,4)(5,6)(7,17)(8,22)(9,14)(10,15)(11,16)(12,20)(13,25)(18,27)(19,29)(21,28)(23,35)(24,31)(26,30)(32,33)(34,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(5,7)(6,12)(8,23)(9,19)(10,20)(11,21)(13,27)(14,17)(15,28)(16,29)(18,26)(22,32)(24,34)(25,33)(30,36)(31,35);(2,4)(5,8,9,24,11,26,10,25)(6,13,15,30,16,31,14,22)(7,18,20,34,21,23,19,33)(12,27,17,32,29,35,28,36);(5,9,11,10)(6,14,16,15)(7,19,21,20)(8,24,26,25)(12,17,29,28)(13,22,31,30)(18,33,23,34)(27,32,35,36)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16518);