Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#12953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #1864 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C22×D8×C73 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
416 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,5,11,7,12,6,24)(3,13,16,28,18,25,17,32)(4,19,21,29,23,9,22,10)(8,20,26,14,27,31,30,15)(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)(2,8,12,27)(4,20)(5,17)(6,16)(7,18)(9,25,19,13)(10,28,29,32)(11,30,24,26)(14,22)(15,21)(23,31);(2,9)(4,21)(5,6)(8,25)(10,24)(11,29)(12,19)(13,27)(14,31)(15,20)(16,17)(22,23)(26,28)(30,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 5941);