Finite Group DatabasebetaFinite Group Databasebeta| order | 24079 |
| automorphism | ? |
| homology | Abelianization (H1) = C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C199⋊C121 |
| derived, Sylow | C199 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | C199⋊C11 |
| commutator, hypocenter | C199 | C121 |
| Fitting, socle, prime radical, cosocle | C11×C199 | C11 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C11 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24079 |
Polycyclic presentation:
11^2,199|a^11=b,c^a=c^125319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24079, 1);