Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#24001 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2404 |
| 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 | |
1122 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)(3,8)(4,15)(5,10)(6,21)(7,12)(9,19)(11,24)(13,29)(14,20)(16,32)(17,31)(18,28)(22,26)(23,27)(25,30)(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);(1,3,7,10)(2,8,12,5)(4,16)(6,14,24,27)(9,25)(11,23,21,20)(13,18)(15,29)(17,26)(19,31)(22,30)(28,32);(1,4)(2,9)(3,13)(5,17)(6,22)(7,18)(8,25)(10,16)(11,28)(12,26)(14,31)(15,21)(19,24)(20,29)(23,32)(27,30);(1,5,7,8)(2,10,12,3)(4,17,18,25)(6,23,24,20)(9,16,26,13)(11,14,21,27)(15,30,28,31)(19,29,22,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16989);