Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#19382 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | C71×#3251 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
594 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)(3,10)(4,8)(5,14)(6,9)(7,11)(12,15)(13,16)(17,18)(19,27)(20,26)(21,23)(22,25)(24,28)(29,32)(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);(1,3,5,11,6,12,4,13)(2,7,8,10,9,16,14,15)(18,23)(24,31)(25,26)(27,32);(1,2)(3,7)(4,14)(5,8)(6,9)(10,11)(12,16)(13,15)(17,19)(18,24)(20,28)(21,29)(22,30)(23,31)(25,27)(26,32);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,16,10)(17,20,21,22)(18,25,23,26)(19,28,29,30)(24,27,31,32)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12370);