Finite Group DatabasebetaFinite Group Databasebeta| order | 31264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#30627615 |
| derived, Sylow | C977 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #16840926 |
| commutator, hypocenter | C977 | C22×C8 |
| Frattini | C2 | C22×#16840926 |
| Fitting | C2×C4×C977 | C4 |
| socle | C22×C977 | C2×C4 |
| prime radical | C22×D977 | C4 |
| cosocle | Dic977 | C23 |
| LCS | G ▷ C977 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15632 |
1984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31264, 229);