Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#3633 |
| unambiguous semidirect product | #595⋊(C4×C8) |
| Fitting | C42×C17 ⋊ C8 |
| derived, Sylow | C17 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #3633 |
| commutator, hypocenter | C17 | C42×C8 |
| Frattini | C22 | C22×#3633 |
| Fitting | C42×C17 | C8 |
| socle | C22×C17 | C22×C8 |
| prime radical | C22×D17 | C22×C4 |
| cosocle | C22×#595 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C42 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #17981067, C4×C8×#3633, C4×#11763893, … |
| maximal normal subgroup of | #17981067, C4×C8×#3633, C4×#11763893, … |
| maximal quotient of | C4×C8×#3633, C4×#11763893, #97×#3633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21642);