Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#25198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,5,10,6,11,21,9)(3,12,15,23,16,25,14,7)(4,17,19,24,20,26,18,8)(13,22,28,31,29,32,30,27)(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);(1,3,5,15,6,16,21,14)(2,7,10,12,11,23,9,25)(4,13,19,28,20,29,18,30)(8,22,17,31,24,32,26,27);(1,4,6,20)(2,8,11,24)(3,13,16,29)(5,18,21,19)(7,22,23,32)(9,17,10,26)(12,27,25,31)(14,28,15,30);(1,2)(3,7)(4,8)(5,10)(6,11)(9,21)(12,15)(13,22)(14,25)(16,23)(17,19)(18,26)(20,24)(27,30)(28,31)(29,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18186);