Finite Group DatabasebetaFinite Group Databasebeta| order | 23148 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D643⋊C9 |
| unambiguous semidirect product | D643⋊(C2×C9) |
| unambiguous semidirect product | (C2×D643)⋊C9 |
| unambiguous semidirect product | (C643⋊C9)⋊C22 |
| unambiguous semidirect product | (C2×C643⋊C9)⋊C2 |
| derived, Sylow | C643 ⋊ C22×C9 |
| Hall | C643⋊C9 ⋊ C22 |
| Hall | C2×D643 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D643⋊C3 |
| commutator, hypocenter | C643 | C22×C9 |
| Frattini | C3 | C2×D643⋊C3 |
| Fitting, socle | C2×C3×C643 | C2×C3 |
| prime radical | C2×C3×D643 | C3 |
| cosocle | C3×C643 | C22×C3 |
| LCS | G ▷ C643 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11574 |
678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23148, 8);