Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C73 · Schur multiplier (H2) = C2 |
| direct product | C73×#7100 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C73 | D8 |
| commutator | C8 | C2×C16×C73 |
| Frattini, cosocle | C82 | C22×C73 |
| socle, prime radical | C22×C73 | #335 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C73 ◁ C4×C8×C73 ◁ C82×C73 ◁ G | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 2 generators on 105 points:
(2,6)(3,7)(4,10)(8,16)(9,14)(11,15)(12,13)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,2,7,13,4,8,11,14,5,9,15,16,10,12,3,6)6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 88);