Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C32×#595 |
| Fitting | C17×C32 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #595 |
| commutator, hypocenter | C17 | C4×C32 |
| Frattini | C16 | C2×#595 |
| Fitting | C17×C32 | C4 |
| socle | C2×C17 | C4×C16 |
| prime radical | C2×D17 | C2×C16 |
| cosocle | C16×D17 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C64×#595, #17949543, C2×C32×#595, … |
| maximal normal subgroup of | C64×#595, #17949543, C2×C32×#595, … |
| maximal quotient of | C32×#3624, #17949096, #17949390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19613);