Finite Group DatabasebetaFinite Group Databasebeta| order | 24990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C17×D49 |
| Fitting, Hall | C3×C5×C17×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C3×C5×C17 |
| Hall | C5×C17×C49 ⋊ C2×C3 |
| Hall | C3×C17×C49 ⋊ C2×C5 |
| Hall | C17×C49 ⋊ C2×C3×C5 |
| Hall | C3×C5×C49 ⋊ C2×C17 |
| Hall | C5×C49 ⋊ C2×C3×C17 |
| Hall | C3×C49 ⋊ C2×C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C17 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C3×C5×C17 |
| Frattini | C7 | C3×C5×D7×C17 |
| Fitting | C3×C5×C17×C49 | C2 |
| socle | C3×C5×C7×C17 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C3×C5×C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12495 |
6630 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24990, 4);