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) = C22 |
| direct product | C17×#1375 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C42 |
| commutator | C4 | C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C22×C17 |
| socle | C22×C17 | #97 |
| prime radical | C23×C17 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,30,26,28,34,35,27,31,33,37,24,29,32,36);(19,21)(23,28,31,29)(25,33)(30,36,37,35)(32,34)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 107);