Finite Group DatabasebetaFinite Group Databasebeta| order | 24805 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C41 ⋊ C5 |
| Sylow | C112 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ #10597243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C41 | C5 |
| LCS | G ▷ C112×C41 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4961 |
Polycyclic presentation:
5,11^2,41|b^a=b^4,c^a=c^4,d^a=d^37997 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24805, 17);