Finite Group DatabasebetaFinite Group Databasebeta| order | 23079 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C157⋊C3 |
| unambiguous semidirect product | C157⋊(C3×C72) |
| Fitting, socle, Hall | C72×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C157⋊C3 |
| commutator, cosocle, hypocenter | C157 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C157 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7693 |
2695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23079, 7);