Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C71 · Schur multiplier (H2) = C210 |
| direct product | C71×#60076 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C71 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C71 |
| Frattini, cosocle | C2×C4 | C25×C71 |
| socle | C2×C71 | C23×C22⋊C4 |
| prime radical | C2×#585×C71 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C22×#41×C71 ◁ G | |
4812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2,6,12,7,11,5,10)(3,13,15,26,16,8,20,22)(4,9,19,25,17,23,18,24)(14,27,29,32,28,21,30,31)(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);(1,3)(2,8)(4,14)(5,15)(6,20)(7,16)(9,21)(10,22)(11,13)(12,26)(17,28)(18,29)(19,30)(23,27)(24,31)(25,32);(1,4)(2,9)(3,14)(5,18)(6,19)(7,17)(8,21)(10,24)(11,23)(12,25)(13,27)(15,29)(16,28)(20,30)(22,31)(26,32);(4,17)(9,23)(14,28)(18,19)(21,27)(24,25)(29,30)(31,32);(1,5,7,6)(2,10,11,12)(3,15,16,20)(4,18,17,19)(8,22,13,26)(9,24,23,25)(14,29,28,30)(21,31,27,32)5822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 53064);