Finite Group DatabasebetaFinite Group Databasebeta| order | 23373 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9×C53 · Schur multiplier (H2) = C1 |
| direct product | C7×C53×C7⋊C9 |
| unambiguous semidirect product | C7⋊(C7×C9×C53) |
| unambiguous semidirect product | (C7×C53)⋊(C7×C9) |
| derived | C7 ⋊ C7×C9×C53 |
| Hall | C72×C53 ⋊ C9 |
| Sylow | C72 ⋊ C9×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C53 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C7×C9×C53 |
| Frattini | C3 | C7×ΓL(1,𝔽8)×C53 |
| Fitting, socle, prime radical | C3×C72×C53 | C3 |
| cosocle | C3×C7 | C3×C7×C53 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C7×C53 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3339 |
5565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23373, 7);