Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C23 |
| direct product | C71×#9529 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #386 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| prime radical | C71×#3109 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 103 points:
(2,6)(3,10)(4,7)(9,14)(11,12)(13,15)(17,18,20,24,22,26,21,25)(19,27,28,23,29,31,30,32)(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);(1,2,7,14,5,9,4,6)(3,8,10,15,12,16,11,13)(17,19)(18,23,26,32)(20,28)(21,30)(22,29)(24,31,25,27);(1,3)(2,8)(4,11)(5,12)(6,13)(7,10)(9,16)(14,15)(18,24)(20,21)(23,31)(25,26)(27,32)(28,30)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 2517);