Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#24409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
1336 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)(3,11,14,7)(4,15)(5,9)(6,10)(8,17)(12,29,30,22)(13,27,20,23)(16,32,31,24)(18,28)(19,26)(21,25)(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)(2,7)(4,16)(5,14)(6,20)(8,24)(9,11)(10,27)(12,18)(13,19)(15,32)(17,31)(21,30)(22,25)(23,26)(28,29);(1,4)(2,8)(3,12)(5,17)(6,21)(7,22)(9,15)(10,28)(11,29)(13,31)(14,30)(16,20)(18,19)(23,32)(24,27)(25,26);(1,3)(2,7)(4,12)(5,14)(6,13)(8,22)(9,11)(10,23)(15,29)(16,18)(17,30)(19,20)(21,31)(24,25)(26,27)(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, 17397);