Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of Dic34 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C24×Dic34 |
| Sylow | C17 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D17 |
| commutator, cosocle | C2×C17 | C26 |
| Frattini | C2 | C25×D17 |
| Fitting | C24×C4×C17 | C2 |
| socle, prime radical | C25×C17 | C22 |
| hypercenter | C24×C4 | D17 |
| hypocenter | C17 | C24×Q8 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
6264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#14527054, #16956709, #16956710, … |
| maximal normal subgroup of | C2×#14527054, #16956709, #16956710, … |
| maximal quotient of | C24×#63225, C24×C4⋊Dic17, C23×C4×Dic34, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19305);