Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#19547 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | #121×C71 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,6,10)(3,7,12,16)(4,9,5,14)(8,13,15,11)(17,18)(19,21)(20,28)(22,27)(23,25)(24,30)(26,31)(29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3)(2,7)(4,13)(5,11)(6,12)(8,14)(9,15)(10,16)(17,19,21,18,23,27,22,25)(20,26,30,24,31,28,29,32);(1,3)(2,8)(4,11)(5,13)(6,12)(7,14)(9,16)(10,15)(17,20)(18,24)(19,26)(21,30)(22,29)(23,31)(25,32)(27,28);(1,4,6,5)(2,9,10,14)(3,11,12,13)(7,8,16,15)(17,21,23,22)(18,19,25,27)(20,29,31,30)(24,28,32,26)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12535);