Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C23 |
| direct product | C71×#23261 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C24 |
| commutator | C23 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| socle, prime radical | C23×C71 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 18176 |
A minimal faithful permutation representation — 4 generators on 103 points:
(2,6)(7,8)(9,10)(11,14)(12,16)(13,15)(17,18,23,19,22,25,21,27)(20,24,29,26,30,32,31,28)(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);(1,2)(3,7)(4,8)(5,6)(9,11,13,12)(10,14,15,16)(17,19,23,25,22,27,21,18)(20,28,29,24,30,26,31,32);(1,3,5,4)(2,7,6,8)(9,12,13,11)(10,14,15,16)(17,20,22,30)(18,24,25,32)(19,26,27,28)(21,31,23,29);(1,4,5,3)(2,7,6,8)(17,21,22,23)(18,19,25,27)(20,29,30,31)(24,28,32,26)4544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16249);