Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C71 · Schur multiplier (H2) = C22 |
| direct product | C71×#10377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C71 |
| prime radical | C24×C71 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2,4,8)(3,11,13,26)(5,19,17,9)(6,10,18,25)(7,22,23,30)(12,20,24,14)(15,28,16,29)(21,32,31,27)(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)(3,12,15,7)(4,8)(5,9)(6,10)(11,14,28,30)(13,24,16,23)(17,19)(18,25)(20,29,22,26)(21,27)(31,32);(1,3,4,16)(2,7,8,24)(5,20,17,30)(6,15,18,13)(9,26,19,28)(10,12,25,23)(11,27,29,32)(14,21,22,31)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 3365);