Finite Group DatabasebetaFinite Group Databasebeta| order | 24964 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C79 |
| unambiguous semidirect product | C79⋊Dic79 |
| derived, Sylow | C792 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C79⋊D79 |
| commutator, hypocenter | C792 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C792 | C2 |
| LCS | G ▷ C792 | |
| UCS | C1 ◁ C2 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24964 |
Polycyclic presentation:
2,79^2,2|a^2=d,b^a=b^78,c^a=c^786244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24964, 7);