Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C16×#3624 |
| derived, Sylow | C17 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #595 |
| commutator, hypocenter | C17 | C8×C16 |
| Frattini | C2×C8 | C2×#595 |
| Fitting | C2×C16×C17 | C4 |
| socle, prime radical | C22×C17 | C4×C8 |
| cosocle | C8×Dic17 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C16 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#3624, #17949088, #17949096, … |
| maximal normal subgroup of | C32×#3624, #17949088, #17949096, … |
| maximal quotient of | C16×#63216, #17948319, #17948487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19419);