Finite Group DatabasebetaFinite Group Databasebeta| order | 31456 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#30628474 |
| Fitting | C2×D4×C983 ⋊ C2 |
| Sylow | C983 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D983 |
| commutator, cosocle | C2×C983 | C24 |
| Frattini | C2 | C23×D983 |
| Fitting | C2×D4×C983 | C2 |
| socle | C22×C983 | C23 |
| hypercenter | C2×D4 | D983 |
| hypocenter | C983 | C2×#41 |
| LCS | G ▷ C2×C983 ▷ C983 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15728 |
4930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31456, 188);