Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C16×#3622 |
| derived, Sylow | C17 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D17 |
| commutator, hypocenter | C17 | C8×C16 |
| Frattini | C4×C8 | C2×D17 |
| Fitting | C4×C16×C17 | C2 |
| socle, prime radical | C22×C17 | C4×C8 |
| cosocle | C4×C8×C17 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C4×C16 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#3622, #16921651, #16921656, … |
| maximal normal subgroup of | C32×#3622, #16921651, #16921656, … |
| maximal quotient of | C16×#63214, #16920939, #16921151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2424);