Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C71 · Schur multiplier (H2) = C27 |
| direct product | C71×#34920 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C71 |
| socle, prime radical | C23×C71 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ G | |
1692 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 18176 |
A minimal faithful permutation representation — 5 generators on 95 points:
(1,2,5,8)(3,7,4,6)(9,10,13,16)(11,15,12,14)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,3,5,4)(2,6,8,7)(9,11,13,12)(10,14,16,15)(17,18)(19,23)(20,21)(22,24);(1,3,5,4)(2,7,8,6)(9,12,13,11)(10,15,16,14)(18,21)(22,23);(17,19,20,24)(18,22,21,23);(1,4,5,3)(2,6,8,7)5396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 27908);