Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×#595 |
| unambiguous semidirect product | D17⋊(C24×C4) |
| Fitting, socle | C25×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #595 |
| commutator, hypocenter | C17 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C17 | C4 |
| prime radical | C25×D17 | C2 |
| cosocle | D17 | C26 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C25 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543957, #379×#595, #17963944, … |
| maximal normal subgroup of | C2×#14543957, #379×#595, #17963944, … |
| maximal quotient of | C24×C4×#595, C24×C22⋊#595, C24×C4⋊#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21507);