Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #400×#6923 |
| Fitting | C61×#400 ⋊ C4 |
| Sylow | C61 ⋊ C4×#400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6923 |
| commutator, socle | C23×C61 | C23×C4 |
| Fitting | C61×#400 | C4 |
| prime radical, cosocle | C23×D61 | C24 |
| hypercenter | #400 | #6923 |
| hypocenter | C61 | C4×#400 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #400 | |
1398 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
418 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1098359);