Finite Group DatabasebetaFinite Group Databasebeta| order | 25664 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#15692008 |
| Fitting | C8×C401 ⋊ C8 |
| derived, Sylow | C401 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #15692008 |
| commutator, hypocenter | C401 | C82 |
| Frattini | C4 | C2×#15692008 |
| Fitting | C8×C401 | C8 |
| socle | C2×C401 | C4×C8 |
| prime radical | C2×D401 | C42 |
| cosocle | C4×#13107944 | C22 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3208 |
464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25664, 1632);