Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#23198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | D42 |
| commutator | C2×C4 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| prime radical | C2×#127×C71 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C22×C4×C71 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,4,3)(5,6,10,15,12,16,11,20)(7,9,14,19,17,18,13,8)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,4,2)(5,7,12,17)(6,8,16,19)(9,15,18,20)(10,13,11,14);(5,8,11,18,12,19,10,9)(6,13,15,7,16,14,20,17);(5,9,10,19,12,18,11,8)(6,14,15,17,16,13,20,7)4118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16186);