Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C16×#595 |
| Fitting | C2×C16×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #595 |
| commutator, hypocenter | C17 | C2×C4×C16 |
| Frattini | C8 | C22×#595 |
| Fitting | C2×C16×C17 | C4 |
| socle | C22×C17 | C4×C8 |
| prime radical | C22×D17 | C2×C8 |
| cosocle | C8×D17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C16 | |
216 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #17949390, #17949396, C4×C16×#595, … |
| maximal normal subgroup of | #17949390, #17949396, C4×C16×#595, … |
| maximal quotient of | C2×C16×#3624, C16×#63242, C2×#14543698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20705);