Finite Group DatabasebetaFinite Group Databasebeta| order | 24522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D67⋊C3 |
| unambiguous semidirect product | D67⋊(C3×C61) |
| unambiguous semidirect product | (C67⋊C3)⋊(C2×C61) |
| Fitting, socle, Hall | C61×C67 ⋊ C2×C3 |
| derived, Sylow | C67 ⋊ C2×C3×C61 |
| Hall | C61×C67⋊C3 ⋊ C2 |
| Hall | C61×D67 ⋊ C3 |
| Hall | C67⋊C3 ⋊ C2×C61 |
| Hall | D67 ⋊ C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C2×C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C61×C67 | C2×C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4087 |
1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24522, 13);