Finite Group DatabasebetaFinite Group Databasebeta| order | 24548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C19⋊Dic323 |
| derived, Hall | C17×C192 ⋊ C4 |
| Sylow | C192 ⋊ Dic17 |
| Sylow | C17 ⋊ C19⋊Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊(C19⋊D19) |
| commutator, hypocenter | C17×C192 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C17×C192 | C2 |
| LCS | G ▷ C17×C192 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24548 |
Polycyclic presentation:
2,17,19^2,2|a^2=e,b^a=b^16,c^a=c^18,d^a=d^186140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24548, 13);