Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×C8×#3633 |
| Fitting | C2×C8×C17 ⋊ C8 |
| derived, Sylow | C17 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #3633 |
| commutator, hypocenter | C17 | C2×C82 |
| Frattini | C4 | C22×#3633 |
| Fitting | C2×C8×C17 | C8 |
| socle | C22×C17 | C4×C8 |
| prime radical | C22×D17 | C42 |
| cosocle | C4×#595 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
280 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #17981195, #17981199, #17981269, … |
| maximal normal subgroup of | #17981195, #17981199, #17981269, … |
| maximal quotient of | C4×C8×#3633, C2×(C2×#3633)⋊C8, #17981589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21616);