Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#3624 |
| derived, Sylow | C17 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #595 |
| commutator, hypocenter | C17 | C24×C8 |
| Frattini | C2 | C24×#595 |
| Fitting, socle, prime radical | C25×C17 | C4 |
| cosocle | Dic17 | C25 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C25 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #17956663, C22×#11763675, C2×#14544450, … |
| maximal normal subgroup of | #17956663, C22×#11763675, C2×#14544450, … |
| maximal quotient of | C23×C4×#3624, C23×C22⋊#3624, C23×C4⋊#3624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21493);