Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×C8×#3624 |
| derived, Sylow | C17 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #595 |
| commutator, hypocenter | C17 | C2×C82 |
| Frattini | C2×C4 | C22×#595 |
| Fitting | C22×C8×C17 | C4 |
| socle, prime radical | C23×C17 | C42 |
| cosocle | C4×Dic17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C8 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #17948487, #17948491, #17948623, … |
| maximal normal subgroup of | #17948487, #17948491, #17948623, … |
| maximal quotient of | C4×C8×#3624, C2×#14543606, #17951685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19701);