Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#19023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | C71×#3559 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 103 points:
(2,6)(4,11)(7,15)(8,12)(9,13)(14,16)(17,18,21,24)(19,25,26,32)(20,28,29,23)(22,30,31,27)(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);(1,2)(3,7)(4,12)(5,8)(6,11)(9,14)(10,16)(13,15)(20,29)(23,28)(25,32)(27,30);(1,3,5,10)(2,7,8,16)(4,13,11,9)(6,14,12,15)(17,19)(18,22)(20,30)(21,26)(23,32)(24,31)(25,28)(27,29);(2,8)(6,12)(7,16)(14,15)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12011);