Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#12833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #1807 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#41×C73 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G | |
358 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)(3,14,18,32)(4,19,21,29)(5,15)(6,11)(7,13)(8,16,22,9)(10,23)(12,25)(17,31,26,20)(24,27)(28,30)(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);(1,3,5,16,6,17,23,29,7,18,24,9,25,26,30,19)(2,8,10,14,12,4,15,20,13,22,28,32,11,21,27,31);(1,4)(2,9)(3,15)(5,20)(6,22)(7,21)(8,25)(10,26)(11,29)(12,19)(13,16)(14,30)(17,28)(18,27)(23,32)(24,31)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 5821);