Finite Group DatabasebetaFinite Group Databasebeta| order | 23121 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C367 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×C367 |
| unambiguous semidirect product | C7⋊(C9×C367) |
| derived, Sylow | C7 ⋊ C9×C367 |
| Hall | C7×C367 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C367 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C9×C367 |
| Frattini | C3 | ΓL(1,𝔽8)×C367 |
| Fitting, socle, prime radical | C3×C7×C367 | C3 |
| cosocle | C3×C7 | C3×C367 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C367 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23121 |
5505 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23121, 2);