Finite Group DatabasebetaFinite Group Databasebeta| order | 23068 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×#64408 |
| Fitting, socle, Hall | C73×C79 ⋊ C4 |
| derived, Sylow | C73 ⋊ C4×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | #64408 |
| commutator, hypocenter | C73 | C4×C79 |
| Frattini | C1 | G |
| Fitting, socle | C73×C79 | C4 |
| prime radical | C79×D73 | C2 |
| cosocle | D73 | C2×C79 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C79 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5767 |
1738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23068, 6);