Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#33833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C4×D4×C73 ◁ C8×D4×C73 ◁ G | |
692 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)(7,15)(8,14)(9,23)(11,12)(13,18)(16,28)(17,29)(19,32)(21,22)(24,26)(27,31)(30,36)(33,35)(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)(6,13)(8,16)(9,24)(10,15)(11,26)(12,17)(14,27)(18,23)(19,33)(20,28)(21,35)(22,30)(25,29)(31,32)(34,36);(2,4)(5,8,12,22)(6,14,11,21)(7,16,17,30)(9,19,23,32)(10,20,25,34)(13,27,26,35)(15,28,29,36)(18,31,24,33);(5,9)(6,10)(7,17)(8,19)(11,25)(12,23)(14,20)(15,24)(16,30)(18,29)(21,34)(22,32)(28,33)(31,36)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26821);