Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#33638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×#476 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C2×#135×C73 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
514 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,8)(3,13,15,31)(4,6)(5,17)(9,23,24,27)(10,12)(14,18,20,30)(16,19)(21,25,29,32)(22,28)(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);(1,2,4,8,7,10,6,12)(3,9,14,21,15,24,20,29)(5,11,16,22,19,26,17,28)(13,25,30,23,31,32,18,27);(1,3)(2,9)(4,14)(5,18)(6,20)(7,15)(8,21)(10,24)(11,27)(12,29)(13,16)(17,31)(19,30)(22,25)(23,26)(28,32);(2,10)(8,12)(9,24)(11,26)(21,29)(22,28)(23,27)(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, 26626);