Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×#595 |
| Fitting | C4×C8×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #595 |
| commutator, hypocenter | C17 | C42×C8 |
| Frattini | C2×C4 | C22×#595 |
| Fitting | C4×C8×C17 | C4 |
| socle | C22×C17 | C2×C42 |
| prime radical | C22×D17 | C22×C4 |
| cosocle | C2×C4×D17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C4×C8 | |
408 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #17948521, C82×#595, #322×#595, … |
| maximal normal subgroup of | #17948521, C82×#595, #322×#595, … |
| maximal quotient of | C82×#595, C4×C8×#3624, #322×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20161);