Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#11762528 |
| derived, Sylow | C17 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D17 |
| commutator, hypocenter | C17 | C2×C64 |
| Frattini | C32 | C2×D17 |
| Fitting | C2×C17×C32 | C2 |
| socle, prime radical | C22×C17 | C32 |
| cosocle | C17×C32 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×Dic17, C4×#11762528, #16922128, … |
| maximal normal subgroup of | C64×Dic17, C4×#11762528, #16922128, … |
| maximal quotient of | C4×#11762528, C22⋊#11762528, C4⋊#11762528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2719);