Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#19529 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | #532×C71 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,6,9)(3,10,8,5)(4,7,12,14)(11,16,15,13)(18,22)(19,25)(20,28)(24,30)(26,27)(29,31)(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);(1,3,5,2,6,8,10,9)(4,11,13,7,12,15,16,14)(17,18,20,22,21,24,28,30)(19,23,27,29,26,32,25,31);(1,4)(2,7)(3,11)(5,13)(6,12)(8,15)(9,14)(10,16)(17,19,21,26)(18,23,24,32)(20,27,28,25)(22,29,30,31);(4,12)(7,14)(11,15)(13,16)(18,24)(19,26)(22,30)(25,27)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12517);