Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | #95×#595 |
| Fitting | C17×#95 ⋊ C4 |
| Sylow | C17 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#595 |
| commutator | C2×C17 | C43 |
| Fitting | C17×#95 | C4 |
| socle | C23×C17 | C22×C4 |
| prime radical, cosocle | C23×D17 | C23 |
| hypercenter | #95 | #595 |
| hypocenter | C17 | C4×#95 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #95 | |
752 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #327×#595, #328×#595, #17952066, … |
| maximal normal subgroup of | #327×#595, #328×#595, #17952066, … |
| maximal quotient of | (C2×#595)⋊#95, #336×#595, #17956579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19681);