Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#1830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #381 |
| commutator | C23 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C23×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,23,26,36,41)(20,28,30,42,31,24,35,38)(21,32,34,46,33,25,39,40)(29,37,45,48,44,43,47,49);(18,20,23,31)(19,24,26,28)(21,29,33,44)(22,35,36,30)(25,37,32,43)(27,42,41,38)(34,47,39,45)(40,49,46,48);(18,21)(19,25,26,32)(20,29)(22,34)(23,33)(24,37,28,43)(27,40,41,46)(30,45)(31,44)(35,47)(36,39)(38,48,42,49)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 562);