Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#19085 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#3553 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,11)(4,12)(5,10)(6,9)(7,8)(13,16)(14,15)(17,18,21,23)(19,25,27,32)(20,28,30,24)(22,29,31,26)(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)(2,4)(5,15)(6,12)(7,13)(8,14)(9,16)(10,11)(17,19,21,27)(18,22,23,31)(20,29,30,26)(24,32,28,25);(1,4)(2,3)(5,11)(6,16)(7,14)(8,13)(9,12)(10,15)(17,18)(19,22)(20,28)(21,23)(24,30)(25,29)(26,32)(27,31);(2,8)(4,14)(9,10)(11,16)(18,23)(22,31)(24,28)(25,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12073);