Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C22×C4 |
| direct product | C71×#9281 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #386 |
| commutator | C42 | C22×C4×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| prime radical | C71×#3207 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2)(3,9)(4,12,14,7)(5,11)(6,8)(10,13,16,15)(17,18,21,24)(19,22)(20,23,28,25)(26,31)(27,29)(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);(1,3,9,2,6,11,5,8)(4,10,13,7,14,16,15,12)(17,19)(18,22,24,31)(20,27)(21,26)(23,29,25,30)(28,32);(1,4)(2,7)(3,10)(5,15)(6,14)(8,12)(9,13)(11,16)(18,23)(20,28)(22,29)(24,25)(27,32)(30,31)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 2269);