Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#11184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #386 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| prime radical | C24×C71 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
818 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)(7,17)(8,22,26,31)(9,15)(10,14)(11,16)(12,19)(13,24,32,25)(18,27,35,36)(20,29)(21,28)(23,33,34,30)(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)(6,12,16,29)(8,23,26,34)(9,20,10,19)(13,30,32,33)(14,28,15,17)(18,24,35,25)(22,27,31,36);(2,4)(5,8,9,24,11,26,10,25)(6,13,14,31,16,32,15,22)(7,18,19,34,21,35,20,23)(12,27,17,33,29,36,28,30)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4172);