Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1366 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #333 |
| commutator | C42 | C2×C4×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| prime radical | C22×C17 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×C8×C17 ◁ G | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,34,27,45,43,23,28,36,44,22,25,35,41)(20,29,31,42,37,40,33,48,30,46,47,49,32,24,38,39);(18,20,23,30)(19,24)(21,33,36,38)(22,37,34,32)(25,29)(26,42)(27,46)(28,40)(31,35,47,45)(39,43)(41,48)(44,49)391 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 98);