Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C71 · Schur multiplier (H2) = C28 |
| direct product | C71×#60938 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C71 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×#117×C71 ◁ G | |
1818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 5 generators on 95 points:
(2,5)(3,7)(9,10,12,14)(11,18,19,16)(13,15,21,17)(20,23,24,22)(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);(1,2)(3,6)(4,5)(7,8)(10,14)(15,17)(16,18)(22,23);(2,5)(6,8)(10,15)(13,21)(14,17)(16,22)(18,23)(20,24);(1,3,4,7)(2,6,5,8)(9,11,12,19)(10,16,14,18)(13,20,21,24)(15,22,17,23);(11,19)(16,18)(20,24)(22,23)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 53926);