Finite Group DatabasebetaFinite Group Databasebeta| order | 15477 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13064104⋊C11 |
| Fitting, socle, derived, Hall | C7×C67 ⋊ C3×C11 |
| Hall | C7×C67⋊C11 ⋊ C3 |
| Hall | #13064104 ⋊ C11 |
| Hall | C67⋊C11 ⋊ ΓL(1,𝔽8) |
| Sylow | C67 ⋊ C11×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C67⋊C3)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C67 | C3×C11 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 469 |
Polycyclic presentation:
3,7,11,67|b^a=b^2,d^a=d^29,d^c=d^6469 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13064104⋊C11, #14584196⋊C11, #14584200⋊C11, … |
| maximal normal subgroup of | C2×#13064104⋊C11, #14584196⋊C11, #14584200⋊C11, … |
| maximal quotient of | C2×#13064104⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15477, 10);