Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C2×#21460630 |
| Fitting | C2×C61×#585 ⋊ C2 |
| Sylow | C61 ⋊ C2×H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C25×D61 |
| commutator, cosocle | C2×C61 | C27 |
| Frattini | C2 | C26×D61 |
| Fitting | C2×C61×#585 | C2 |
| socle | C22×C61 | C26 |
| hypercenter | C2×#585 | D61 |
| hypocenter | C61 | C2×H(7,𝔽2) |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×#585 | |
60570 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
2170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1083465);