Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C27 |
| direct product | C71×#23876 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
2012 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 4 generators on 83 points:
(6,10)(7,8)(11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,2)(3,4)(5,6)(7,12)(8,10)(9,11);(2,4)(5,6)(7,10)(8,12)(9,11);(5,6)(7,12)(8,10)(9,11)3053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16864);