Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1398 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C42 |
| commutator | C4 | C4×C8×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| socle | C2×C17 | #346 |
| prime radical | C22×C17 | M32 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ G | |
60 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)(18,19,20,25,21,27,30,40,22,28,31,38,32,42,44,48,23,26,29,39,33,41,43,49,34,24,35,36,45,37,46,47);(19,24,26,28)(20,29)(25,38,39,36)(27,37,41,42)(30,43)(31,35)(40,48,49,47)(44,46)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 130);