Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#11182 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #397 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| prime radical | C24×C71 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 107 points:
(5,6,10,16,11,14,9,15)(7,17,20,28,21,12,19,29)(8,22,24,31,26,32,25,13)(18,34,35,27,36,30,23,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,2)(3,4)(5,7,11,21)(6,12,14,17)(8,23,26,35)(9,20,10,19)(13,30,31,34)(15,29,16,28)(18,24,36,25)(22,27,32,33);(2,4)(5,8)(6,13,14,31)(7,18)(9,24)(10,25)(11,26)(12,27,17,33)(15,22,16,32)(19,35)(20,23)(21,36)(28,30,29,34)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4170);