Finite Group DatabasebetaFinite Group Databasebeta| order | 24108 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic123 |
| unambiguous semidirect product | C3⋊(C49×Dic41) |
| derived, Hall | C3×C41 ⋊ C4×C49 |
| Hall | C3×C41×C49 ⋊ C4 |
| Hall | C41×C49 ⋊ Dic3 |
| Hall | C3×C49 ⋊ Dic41 |
| Sylow | C41 ⋊ Dic3×C49 |
| Sylow | C3 ⋊ C49×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D123 |
| commutator, hypocenter | C3×C41 | C4×C49 |
| Frattini | C2×C7 | C7×D123 |
| Fitting | C2×C3×C41×C49 | C2 |
| socle, prime radical, cosocle | C2×C3×C7×C41 | C2×C7 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24108 |
6174 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24108, 10);