Finite Group DatabasebetaFinite Group Databasebeta| order | 27005 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C491 ⋊ C5 |
| Sylow | C491 ⋊ C11⋊C5 |
| Sylow | C11 ⋊ C491⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C491 | C5 |
| LCS | G ▷ C11×C491 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5401 |
Polycyclic presentation:
5,11,491|b^a=b^5,c^a=c^1011085 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27005, 5);