Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#3624 |
| derived, Sylow | C17 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #595 |
| commutator, hypocenter | C17 | C42×C8 |
| Frattini | C23 | C22×#595 |
| Fitting | C2×C42×C17 | C4 |
| socle, prime radical | C23×C17 | C22×C4 |
| cosocle | C22×Dic17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C42 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #17948231, C4×C8×#3624, C4×#11763650, … |
| maximal normal subgroup of | #17948231, C4×C8×#3624, C4×#11763650, … |
| maximal quotient of | C4×C8×#3624, C4×#11763650, #97×#3624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20162);