Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G | |
1102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,12)(4,9)(5,18)(6,16)(7,11)(8,14)(10,21)(13,29)(15,30)(17,20)(19,24)(22,31)(23,27)(25,28)(26,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3)(2,8)(4,13)(5,19)(6,23)(7,15)(9,24)(10,27)(11,25)(12,18)(14,21)(16,26)(17,28)(20,29)(22,32)(30,31);(1,2)(3,8)(4,16)(5,20)(6,9)(7,11)(10,22)(12,28)(13,26)(14,30)(15,25)(17,18)(19,29)(21,31)(23,24)(27,32);(1,4,7,6)(2,9,11,16)(3,13,15,23)(5,17,22,21)(8,24,25,26)(10,18,20,31)(12,29,30,27)(14,19,28,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26521);