Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D17×D32 |
| Fitting | C17×D32 ⋊ C2 |
| Sylow | C17 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D17 |
| commutator, cosocle | C16×C17 | C23 |
| Frattini | C16 | C22×D17 |
| Fitting | C17×D32 | C2 |
| socle | C2×C17 | C2×D16 |
| hypercenter | D32 | D17 |
| hypocenter | C17 | C2×D32 |
| LCS | G ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D64, D17×SD128, #16955380, … |
| maximal normal subgroup of | D17×D64, D17×SD128, #16955380, … |
| maximal quotient of | D17×#1415, D17×#1423, #16954895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6806);