Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1335 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | D8 |
| commutator | C8 | C2×C8×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| socle | C2×C17 | D4⋊C8 |
| prime radical | C17×#135 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C2×C8×C17 ◁ C4×C8×C17 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,24,28,33,26,25,29,21,32,23,20,30,31);(18,20)(19,24)(21,26)(22,31)(23,29)(25,28)(27,33)(30,32)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 67);