Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33570 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C73 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G | |
1212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1168 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,14)(12,16)(13,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(2,7)(3,4)(5,14)(8,15)(9,11)(10,16);(2,8)(5,14)(7,15)(9,16)(10,11)(12,13);(1,3,6,4)(2,9,11,7)(5,12,14,13)(8,16,10,15)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26558);