Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C2×C73×#3415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C25×C73 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×#41×C73 ◁ C2×#131×C73 ◁ G | |
2126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(3,4)(5,10)(6,9)(7,20)(8,13)(11,17)(12,18)(14,24)(15,21)(16,30)(19,23)(22,31)(25,29)(26,28)(27,32)(33,34);(4,9)(6,17)(7,18)(10,21)(11,12)(13,23)(15,29)(16,28)(19,31)(20,22)(24,32)(25,26)(27,34)(30,33);(3,5)(4,10)(6,15)(7,16)(8,14)(9,21)(11,25)(12,26)(13,24)(17,29)(18,28)(19,27)(20,30)(22,33)(23,32)(31,34);(5,14)(10,24)(15,27)(16,28)(21,32)(25,33)(26,30)(29,34)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 55620);