Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#23723 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C71 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| socle | C2×C71 | C2×#399 |
| prime radical | C22×#41×C71 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C23×C4×C71 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,5,9,6,10,12,20)(3,11,14,22,15,26,19,7)(4,16,18,30,17,8,23,25)(13,27,29,24,28,32,31,21)(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);(1,3,12,14,6,15,5,19)(2,7,20,11,10,22,9,26)(4,13,23,29,17,28,18,31)(8,24,30,32,16,21,25,27);(1,4)(2,8)(3,13)(5,18)(6,17)(7,21)(9,25)(10,16)(11,27)(12,23)(14,29)(15,28)(19,31)(20,30)(22,24)(26,32);(4,17)(8,16)(13,28)(18,23)(21,24)(25,30)(27,32)(29,31)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16711);