Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| isoclinism | isoclinic class of #92470 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D248 |
| Fitting | C23×C8×C31 ⋊ C2 |
| Sylow | C31 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D124 |
| commutator, cosocle | C4×C31 | C25 |
| Frattini | C4 | C24×D31 |
| Fitting | C23×C8×C31 | C2 |
| socle | C24×C31 | D4 |
| hypercenter | C23×C8 | D31 |
| hypocenter | C31 | C23×D8 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
1016 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 19226);