Finite Group DatabasebetaFinite Group Databasebeta| order | 32048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D2003 |
| unambiguous semidirect product | C2003⋊C24 |
| unambiguous semidirect product | (C2×C2003)⋊C23 |
| Fitting, socle | C23×C2003 ⋊ C2 |
| derived, Sylow | C2003 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D2003 |
| commutator, cosocle, hypocenter | C2003 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C2003 | C2 |
| LCS | G ▷ C2003 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16024 |
8024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32048, 42);