Finite Group DatabasebetaFinite Group Databasebeta| order | 24079 |
| automorphism | ? |
| homology | Abelianization (H1) = C112 · Schur multiplier (H2) = C11 |
| direct product | C11×C199⋊C11 |
| unambiguous semidirect product | C199⋊C112 |
| unambiguous semidirect product | (C11×C199)⋊C11 |
| Fitting, socle | C11×C199 ⋊ C11 |
| derived, Sylow | C199 ⋊ C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C199⋊C11 |
| commutator, cosocle, hypocenter | C199 | C112 |
| Frattini | C1 | G |
| Fitting, socle | C11×C199 | C11 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C11 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2189 |
319 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24079, 3);