Finite Group DatabasebetaFinite Group Databasebeta| order | 8305 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C151 ⋊ C5 |
| Sylow | C151 ⋊ C11⋊C5 |
| Sylow | C11 ⋊ C151⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C151 | C5 |
| LCS | G ▷ C11×C151 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
5,11,151|b^a=b^5,c^a=c^8337 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22552175, #30658860, #30658866, … |
| maximal normal subgroup of | C2×#22552175, #30658860, #30658866, … |
| maximal quotient of | C2×#22552175, C3×#22552175 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8305, 5);