Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C27 |
| direct product | C73×#23892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
1674 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)(3,13)(4,19)(5,23)(6,11)(7,12)(8,16)(9,21)(10,20)(14,30)(15,25)(17,27)(18,26)(22,29)(24,31)(28,32)(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)(4,15)(5,17)(6,16)(7,18)(9,28)(10,25)(11,26)(12,27)(13,23)(14,20)(19,24)(21,31)(22,32)(29,30);(1,4)(2,9)(3,14)(5,20)(6,21)(7,22)(8,24)(10,12)(11,29)(13,25)(15,16)(17,32)(18,31)(19,23)(26,28)(27,30);(1,4)(2,10)(3,15)(5,21)(6,20)(7,22)(8,25)(9,12)(11,29)(13,24)(14,16)(17,31)(18,32)(19,23)(26,30)(27,28)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16880);