Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×#63242 |
| derived, Sylow | C17 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #595 |
| commutator, hypocenter | C17 | C24×C8 |
| Frattini | C2 | C24×#595 |
| Fitting | C23×C4×C17 | C4 |
| socle | C24×C17 | C2×C4 |
| prime radical | C24×D17 | C4 |
| cosocle | Dic17 | C25 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C23×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #17956661, #17956664, #17956685, … |
| maximal normal subgroup of | #17956661, #17956664, #17956685, … |
| maximal quotient of | C23×C4×#3624, C22×C4×#63242, C22×#11763777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21494);