Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C16×#3633 |
| Fitting | C16×C17 ⋊ C8 |
| derived, Sylow | C17 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #3633 |
| commutator, hypocenter | C17 | C8×C16 |
| Frattini | C8 | C2×#3633 |
| Fitting | C16×C17 | C8 |
| socle | C2×C17 | C82 |
| prime radical | C2×D17 | C4×C8 |
| cosocle | C8×#595 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C16 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#3633, #17981334, C2×C16×#3633, … |
| maximal normal subgroup of | C32×#3633, #17981334, C2×C16×#3633, … |
| maximal quotient of | C16×#63241, #17981091, #17981195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21523);