Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×Dic17 |
| derived, Sylow | C17 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D17 |
| commutator, hypocenter | C17 | C42×C8 |
| Frattini | C22×C4 | C22×D17 |
| Fitting | C2×C4×C8×C17 | C2 |
| socle, prime radical | C23×C17 | C22×C4 |
| cosocle | C22×C4×C17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C4×C8 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16921179, C82×Dic17, #322×Dic17, … |
| maximal normal subgroup of | #16921179, C82×Dic17, #322×Dic17, … |
| maximal quotient of | C82×Dic17, C4×C8×#3622, #322×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4191);